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Mon Aug 26 13:04:31 MDT 2024
J. M. Peña Strict Diagonal Dominance and Optimal
Bounds for the Skeel Condition Number 1107--1108
Long Chen A New Class of High Order Finite Volume
Methods for Second Order Elliptic
Equations . . . . . . . . . . . . . . . 4021--4043
Yingda Cheng and
Chi-Wang Shu Superconvergence of Discontinuous
Galerkin and Local Discontinuous
Galerkin Schemes for Linear Hyperbolic
and Convection--Diffusion Equations in
One Space Dimension . . . . . . . . . . 4044--4072
Qiqi Wang and
Parviz Moin and
Gianluca Iaccarino A Rational Interpolation Scheme with
Superpolynomial Rate of Convergence . . 4073--4097
Zhiqiang Cai and
JaEun Ku Optimal Error Estimate for the Div
Least-squares Method with Data $ f \in
L^2 $ and Application to Nonlinear
Problems . . . . . . . . . . . . . . . . 4098--4111
Mark Ainsworth and
Richard Rankin Fully Computable Error Bounds for
Discontinuous Galerkin Finite Element
Approximations on Meshes with an
Arbitrary Number of Levels of Hanging
Nodes . . . . . . . . . . . . . . . . . 4112--4141
Hyea Hyun Kim and
Chang-Ock Lee and
Eun-Hee Park A FETI-DP Formulation for the Stokes
Problem without Primal Pressure
Components . . . . . . . . . . . . . . . 4142--4162
Yves Coudi\`ere and
Gianmarco Manzini The Discrete Duality Finite Volume
Method for Convection-diffusion Problems 4163--4192
O. Angelini and
C. Chavant and
E. Chénier and
R. Eymard A Finite Volume Scheme for Diffusion
Problems on General Meshes Applying
Monotony Constraints . . . . . . . . . . 4193--4213
L. Beirão da Veiga and
C. Chinosi and
C. Lovadina and
L. F. Pavarino Robust BDDC Preconditioners for
Reissner--Mindlin Plate Bending Problems
and MITC Elements . . . . . . . . . . . 4214--4238
Yanzhao Cao and
Max Gunzburger and
Xiaolong Hu and
Fei Hua and
Xiaoming Wang and
Weidong Zhao Finite Element Approximations for
Stokes--Darcy Flow with Beavers--Joseph
Interface Conditions . . . . . . . . . . 4239--4256
Liqun Cao and
Ya Zhang and
Walter Allegretto and
Yanping Lin Multiscale Asymptotic Method for
Maxwell's Equations in Composite
Materials . . . . . . . . . . . . . . . 4257--4289
Shoufu Li High Order Contractive Runge--Kutta
Methods for Volterra Functional
Differential Equations . . . . . . . . . 4290--4325
Daan Huybrechs On the Fourier Extension of Nonperiodic
Functions . . . . . . . . . . . . . . . 4326--4355
Richard Norton and
Robert Scheichl Convergence Analysis of Planewave
Expansion Methods for $2$D Schrödinger
Operators with Discontinuous Periodic
Potentials . . . . . . . . . . . . . . . 4356--4380
Hong-lin Liao and
Zhi-zhong Sun and
Han-sheng Shi Error Estimate of Fourth-Order Compact
Scheme for Linear Schrödinger Equations 4381--4401
Miodrag S. Petkovi\'c On a General Class of Multipoint
Root-Finding Methods of High
Computational Efficiency . . . . . . . . 4402--4414
Michael Döhler and
Stefan Kunis and
Daniel Potts Nonequispaced Hyperbolic Cross Fast
Fourier Transform . . . . . . . . . . . 4415--4428
Ch. Eck and
B. Jadamba and
P. Knabner Error Estimates for a Finite Element
Discretization of a Phase Field Model
for Mixtures . . . . . . . . . . . . . . 4429--4445
Jun Hu and
Yunqing Huang A Posteriori Error Analysis of Finite
Element Methods for Reissner--Mindlin
Plates . . . . . . . . . . . . . . . . . 4446--4472
Dietrich Braess and
Pingbing Ming and
Zhong-ci Shi Shear Locking in a Plane Elasticity
Problem and the Enhanced Assumed Strain
Method . . . . . . . . . . . . . . . . . 4473--4491
Huangxin Chen and
Xuejun Xu Local Multilevel Methods for Adaptive
Finite Element Methods for Nonsymmetric
and Indefinite Elliptic Boundary Value
Problems . . . . . . . . . . . . . . . . 4492--4516
G. Bencteux and
E. Cancés and
W. W. Hager and
C. Le Bris Analysis of a Quadratic Programming
Decomposition Algorithm . . . . . . . . 4517--4539
Xuejun Xu and
Lizhen Qin Spectral Analysis of Dirichlet--Neumann
Operators and Optimized Schwarz Methods
with Robin Transmission Conditions . . . 4540--4568
Wolfgang Boiger and
Carsten Carstensen On the Strong Convergence of Gradients
in Stabilized Degenerate Convex
Minimization Problems . . . . . . . . . 4569--4580
C. V. Pao and
Xin Lu Block Monotone Iterative Method for
Semilinear Parabolic Equations with
Nonlinear Boundary Conditions . . . . . 4581--4606
Matthias Heinkenschloss and
Dmitriy Leykekhman Local Error Estimates for SUPG Solutions
of Advection-Dominated Elliptic
Linear-Quadratic Optimal Control
Problems . . . . . . . . . . . . . . . . 4607--4638
Roland Becker and
Shipeng Mao and
Zhongci Shi A Convergent Nonconforming Adaptive
Finite Element Method with Quasi-Optimal
Complexity . . . . . . . . . . . . . . . 4639--4659
Rob Haelterman and
Joris Degroote and
Dirk Van Heule and
Jan Vierendeels On the Similarities Between the
Quasi-Newton Inverse Least Squares
Method and GMRes . . . . . . . . . . . . 4660--4679
Noel J. Walkington Compactness Properties of the DG and CG
Time Stepping Schemes for Parabolic
Equations . . . . . . . . . . . . . . . 4680--4710
Afef Sellami Quantization Based Filtering Method
Using First Order Approximation . . . . 4711--4734
Qingxiang Xu and
Yimin Wei and
Yangyang Gu Sharp Norm-Estimations for
Moore--Penrose Inverses of Stable
Perturbations of Hilbert $ C^* $-Module
Operators . . . . . . . . . . . . . . . 4735--4758
Michael Griebel and
Markus Hegland A Finite Element Method for Density
Estimation with Gaussian Process Priors 4759--4792
Shuhuang Xiang Correction to ``Strict Diagonal
Dominance and Optimal Bounds for the
Skeel Condition Number'' . . . . . . . . 4793--4795
S. Bellavia and
C. Cartis and
N. I. M. Gould and
B. Morini and
Ph. L. Toint Convergence of a Regularized Euclidean
Residual Algorithm for Nonlinear
Least-Squares . . . . . . . . . . . . . 1--29
Zhiqiang Cai and
Shun Zhang Recovery-Based Error Estimators for
Interface Problems: Mixed and
Nonconforming Finite Elements . . . . . 30--52
Jean-Luc Guermond and
Guido Kanschat Asymptotic Analysis of Upwind
Discontinuous Galerkin Approximation of
the Radiative Transport Equation in the
Diffusive Limit . . . . . . . . . . . . 53--78
Zhiqiang Cai and
Chunbo Wang and
Shun Zhang Mixed Finite Element Methods for
Incompressible Flow: Stationary
Navier--Stokes Equations . . . . . . . . 79--94
S. Sauter $ h p$-Finite Elements for Elliptic
Eigenvalue Problems: Error Estimates
Which Are Explicit with Respect to $
\lambda $, $h$, and $p$ . . . . . . . . 95--108
Georgios Akrivis and
Panagiotis Chatzipantelidis A Posteriori Error Estimates for the
Two-Step Backward Differentiation
Formula Method for Parabolic Equations 109--132
Bernardo Cockburn and
Bo Dong and
Johnny Guzmán and
Jianliang Qian Optimal Convergence of the Original DG
Method on Special Meshes for Variable
Transport Velocity . . . . . . . . . . . 133--146
Benqi Guo and
Ivo Babu\vska Local Jacobi Operators and Applications
to the $p$-Version of Finite Element
Method in Two Dimensions . . . . . . . . 147--163
Erich Carelli and
Jonas Haehnle and
Andreas Prohl Convergence Analysis for Incompressible
Generalized Newtonian Fluid Flows with
Nonstandard Anisotropic Growth
Conditions . . . . . . . . . . . . . . . 164--190
Gang Wu and
Yimin Wei On Analysis of Projection Methods for
Rational Function Approximation to the
Matrix Exponential . . . . . . . . . . . 191--197
Alexandre Ern and
Martin Vohralík A Posteriori Error Estimation Based on
Potential and Flux Reconstruction for
the Heat Equation . . . . . . . . . . . 198--223
Jérémie Bigot and
Sébastien Gadat Smoothing under Diffeomorphic
Constraints with Homeomorphic Splines 224--243
Drahoslava Janovská and
Gerhard Opfer A Note on the Computation of All Zeros
of Simple Quaternionic Polynomials . . . 244--256
Emmanuel Gobet and
Céline Labart Solving BSDE with Adaptive Control
Variate . . . . . . . . . . . . . . . . 257--277
Nawaf Bou-Rabee and
Houman Owhadi Long-Run Accuracy of Variational
Integrators in the Stochastic Context 278--297
Evelyn Buckwar and
Cónall Kelly Towards a Systematic Linear Stability
Analysis of Numerical Methods for
Systems of Stochastic Differential
Equations . . . . . . . . . . . . . . . 298--321
S. L. Cotter and
M. Dashti and
A. M. Stuart Approximation of Bayesian Inverse
Problems for PDEs . . . . . . . . . . . 322--345
Mark Ainsworth and
Hafiz Abdul Wajid Optimally Blended Spectral-Finite
Element Scheme for Wave Propagation and
Nonstandard Reduced Integration . . . . 346--371
Annegret Glitzky and
Jens A. Griepentrog Discrete Sobolev--Poincaré Inequalities
for Voronoi Finite Volume Approximations 372--391
M. Bellalij and
Y. Saad and
H. Sadok Further Analysis of the Arnoldi Process
for Eigenvalue Problems . . . . . . . . 393--407
Mihály Kovács and
Stig Larsson and
Fardin Saedpanah Finite Element Approximation of the
Linear Stochastic Wave Equation with
Additive Noise . . . . . . . . . . . . . 408--427
Sonja Cox and
Jan van Neerven Convergence Rates of the Splitting
Scheme for Parabolic Linear Stochastic
Cauchy Problems . . . . . . . . . . . . 428--451
Javier Segura Reliable Computation of the Zeros of
Solutions of Second Order Linear ODEs
Using a Fourth Order Method . . . . . . 452--469
Alan Demlow Convergence of an Adaptive Finite
Element Method for Controlling Local
Energy Errors . . . . . . . . . . . . . 470--497
Ivo Babu\vska and
Gabriel N. Gatica A Residual-Based a Posteriori Error
Estimator for the Stokes--Darcy Coupled
Problem . . . . . . . . . . . . . . . . 498--523
S. Loisel and
J. Côté and
M. J. Gander and
L. Laayouni and
A. Qaddouri Optimized Domain Decomposition Methods
for the Spherical Laplacian . . . . . . 524--551
Jonathan C. Mattingly and
Andrew M. Stuart and
M. V. Tretyakov Convergence of Numerical Time-Averaging
and Stationary Measures via Poisson
Equations . . . . . . . . . . . . . . . 552--577
Zhiqiang Cai and
Shun Zhang Flux Recovery and a Posteriori Error
Estimators: Conforming Elements for
Scalar Elliptic Equations . . . . . . . 578--602
Carlo Lovadina and
David Mora and
Rodolfo Rodríguez Approximation of the Buckling Problem
for Reissner--Mindlin Plates . . . . . . 603--632
Giovanni Samaey and
Wim Vanroose An Analysis of Equivalent Operator
Preconditioning for Equation-Free
Newton--Krylov Methods . . . . . . . . . 633--658
Petr Knobloch A Generalization of the Local Projection
Stabilization for
Convection--Diffusion-Reaction Equations 659--680
Kaixin Wang and
Hong Wang An Optimal-Order Error Estimate to ELLAM
Schemes for Transient
Advection--Diffusion Equations on
Unstructured Meshes . . . . . . . . . . 681--707
Fei Wang and
Weimin Han and
Xiao-liang Cheng Discontinuous Galerkin Methods for
Solving Elliptic Variational
Inequalities . . . . . . . . . . . . . . 708--733
Andrea Bonito and
Ricardo H. Nochetto Quasi-Optimal Convergence Rate of an
Adaptive Discontinuous Galerkin Method 734--771
Xiangxiong Zhang and
Chi-Wang Shu A Genuinely High Order Total Variation
Diminishing Scheme for One-Dimensional
Scalar Conservation Laws . . . . . . . . 772--795
Todd Arbogast and
Wen-Hao Wang Convergence of a Fully Conservative
Volume Corrected Characteristic Method
for Transport Problems . . . . . . . . . 797--823
Ming Cui and
Xiu Ye Unified Analysis of Finite Volume
Methods for the Stokes Equations . . . . 824--839
Andreas App and
Ulrich Reif Piecewise Linear Orthogonal
Approximation . . . . . . . . . . . . . 840--856
B. Cockburn and
J. Gopalakrishnan and
F. Li and
N.-C. Nguyen and
J. Peraire Hybridization and Postprocessing
Techniques for Mixed Eigenfunctions . . 857--881
Mike Giles and
Stefan Ulbrich Convergence of Linearized and Adjoint
Approximations for Discontinuous
Solutions of Conservation Laws. Part 1:
Linearized Approximations and Linearized
Output Functionals . . . . . . . . . . . 882--904
Mike Giles and
Stefan Ulbrich Convergence of Linearized and Adjoint
Approximations for Discontinuous
Solutions of Conservation Laws. Part 2:
Adjoint Approximations and Extensions 905--921
Andreas Rößler Runge--Kutta Methods for the Strong
Approximation of Solutions of Stochastic
Differential Equations . . . . . . . . . 922--952
Javier de Frutos and
Bosco García-Archilla and
Julia Novo Stabilization of Galerkin Finite Element
Approximations to Transient
Convection--Diffusion Problems . . . . . 953--979
Siobhan Burke and
Christoph Ortner and
Endre Süli An Adaptive Finite Element Approximation
of a Variational Model of Brittle
Fracture . . . . . . . . . . . . . . . . 980--1012
Santiago Badia and
Ramon Codina and
Juan Vicente Gutiérrez-Santacreu Long-Term Stability Estimates and
Existence of a Global Attractor in a
Finite Element Approximation of the
Navier--Stokes Equations with Numerical
Subgrid Scale Modeling . . . . . . . . . 1013--1037
Qiang Zhang and
Chi-Wang Shu Stability Analysis and a Priori Error
Estimates of the Third Order Explicit
Runge--Kutta Discontinuous Galerkin
Method for Scalar Conservation Laws . . 1038--1063
Ismaël F. Bailleul and
Peter L. W. Man and
Markus Kraft A Stochastic Algorithm for Parametric
Sensitivity in Smoluchowski's
Coagulation Equation . . . . . . . . . . 1064--1086
Jie Shen and
Li-Lian Wang Sparse Spectral Approximations of
High-Dimensional Problems Based on
Hyperbolic Cross . . . . . . . . . . . . 1087--1109
Imran H. Biswas and
Espen R. Jakobsen and
Kenneth H. Karlsen Difference-Quadrature Schemes for
Nonlinear Degenerate Parabolic
Integro-PDE . . . . . . . . . . . . . . 1110--1135
Yves Achdou and
Italo Capuzzo-Dolcetta Mean Field Games: Numerical Methods . . 1136--1162
Wenbin Liu and
Danping Yang and
Lei Yuan and
Chaoqun Ma Finite Element Approximations of an
Optimal Control Problem with Integral
State Constraint . . . . . . . . . . . . 1163--1185
Dongho Kim and
Eun-Jae Park A Priori and a Posteriori Analysis of
Mixed Finite Element Methods for
Nonlinear Elliptic Equations . . . . . . 1186--1207
Bangti Jin and
Dirk A. Lorenz Heuristic Parameter-Choice Rules for
Convex Variational Regularization Based
on Error Estimates . . . . . . . . . . . 1208--1229
Xin-min Xiang and
Zhong-qing Wang Generalized Hermite Spectral Method and
its Applications to Problems in
Unbounded Domains . . . . . . . . . . . 1231--1253
Carla Manni and
Marie-Laurence Mazure Shape Constraints and Optimal Bases for
$ C^1 $ Hermite Interpolatory
Subdivision Schemes . . . . . . . . . . 1254--1280
Ross Ingram and
Mary F. Wheeler and
Ivan Yotov A Multipoint Flux Mixed Finite Element
Method on Hexahedra . . . . . . . . . . 1281--1312
C. Bost and
G.-H. Cottet and
E. Maitre Convergence Analysis of a Penalization
Method for the Three-Dimensional Motion
of a Rigid Body in an Incompressible
Viscous Fluid . . . . . . . . . . . . . 1313--1337
Gabriel N. Gatica and
George C. Hsiao and
Salim Meddahi A Coupled Mixed Finite Element Method
for the Interaction Problem between an
Electromagnetic Field and an Elastic
Body . . . . . . . . . . . . . . . . . . 1338--1368
Weidong Zhao and
Guannan Zhang and
Lili Ju A Stable Multistep Scheme for Solving
Backward Stochastic Differential
Equations . . . . . . . . . . . . . . . 1369--1394
Martin Healey and
Norbert Heuer Mortar Boundary Elements . . . . . . . . 1395--1418
L. Beirão da Veiga and
K. Lipnikov and
G. Manzini Error Analysis for a Mimetic
Discretization of the Steady Stokes
Problem on Polyhedral Meshes . . . . . . 1419--1443
Hong Wang and
Kaixin Wang Uniform Estimates of an
Eulerian--Lagrangian Method for
Time-Dependent Convection--Diffusion
Equations in Multiple Space Dimensions 1444--1473
Jian-Guo Liu and
Luc Mieussens Analysis of an Asymptotic Preserving
Scheme for Linear Kinetic Equations in
the Diffusion Limit . . . . . . . . . . 1474--1491
C. Yalçin Kaya Inexact Restoration for Runge--Kutta
Discretization of Optimal Control
Problems . . . . . . . . . . . . . . . . 1492--1517
A. Bespalov and
N. Heuer and
R. Hiptmair Convergence of the Natural $ h p$-BEM
for the Electric Field Integral Equation
on Polyhedral Surfaces . . . . . . . . . 1518--1529
Wenbin Chen and
Xingjie Li and
Dong Liang Energy-Conserved Splitting
Finite-Difference Time-Domain Methods
for Maxwell's Equations in Three
Dimensions . . . . . . . . . . . . . . . 1530--1554
Eric A. Machorro Discontinuous Finite Elements for a
Hyperbolic Problem with Singular
Coefficient: a Convergence Theory for
One-Dimensional Spherical Transport . . 1555--1578
Xiaoyuan Yang and
Yuanyuan Duan and
Yuhua Guo A Posteriori Error Estimates for Finite
Element Approximation of Unsteady
Incompressible Stochastic Navier--Stokes
Equations . . . . . . . . . . . . . . . 1579--1600
Pawe\l D\lotko and
Ruben Specogna Critical Analysis of the Spanning Tree
Techniques . . . . . . . . . . . . . . . 1601--1624
Alexander Mielke and
Laetitia Paoli and
Adrien Petrov and
Ulisse Stefanelli Error Estimates for Space--time
Discretizations of a Rate-Independent
Variational Inequality . . . . . . . . . 1625--1646
José Trashorras and
Dimitrios K. Tsagkarogiannis From Mesoscale Back to Microscale:
Reconstruction Schemes for
Coarse-Grained Stochastic Lattice
Systems . . . . . . . . . . . . . . . . 1647--1677
C. Chalons and
F. Coquel and
C. Marmignon Time-Implicit Approximation of the
Multipressure Gas Dynamics Equations in
Several Space Dimensions . . . . . . . . 1678--1706
B. Aylaj and
A. Noussair Convergence of Numerical Schemes to a
Nonlinear Kinetic Model of Population
Dynamics with Nonlocal Boundary
Conditions . . . . . . . . . . . . . . . 1707--1732
François Bouchut and
Tomás Morales de Luna A Subsonic-Well-Balanced Reconstruction
Scheme for Shallow Water Flows . . . . . 1733--1758
Kun Zhou and
Qiang Du Mathematical and Numerical Analysis of
Linear Peridynamic Models with Nonlocal
Boundary Conditions . . . . . . . . . . 1759--1780
R. V. Kohn and
H. M. Versieux Numerical Analysis of a Steepest-Descent
PDE Model for Surface Relaxation below
the Roughening Temperature . . . . . . . 1781--1800
Gabriel R. Barrenechea and
Frédéric Valentin Consistent Local Projection Stabilized
Finite Element Methods . . . . . . . . . 1801--1825
Volker Grimm and
Martin Gugat Approximation of Semigroups and Related
Operator Functions by Resolvent Series 1826--1845
Kenneth H. Karlsen and
Trygve K. Karper A Convergent Nonconforming Finite
Element Method for Compressible Stokes
Flow . . . . . . . . . . . . . . . . . . 1846--1876
A. Bonito and
R. H. Nochetto and
M. S. Pauletti Geometrically Consistent Mesh
Modification . . . . . . . . . . . . . . 1877--1899
M. Colombeau A Method of Projection of Delta Waves in
a Godunov Scheme and Application to
Pressureless Fluid Dynamics . . . . . . 1900--1919
Huayi Wei and
Long Chen and
Yunqing Huang Superconvergence and Gradient Recovery
of Linear Finite Elements for the
Laplace--Beltrami Operator on General
Surfaces . . . . . . . . . . . . . . . . 1920--1943
Hermann Brunner and
Qiumei Huang and
Hehu Xie Discontinuous Galerkin Methods for Delay
Differential Equations of Pantograph
Type . . . . . . . . . . . . . . . . . . 1944--1967
Youngmok Jeon and
Eun-Jae Park A Hybrid Discontinuous Galerkin Method
for Elliptic Problems . . . . . . . . . 1968--1983
L. Bos and
S. De Marchi and
A. Sommariva and
M. Vianello Computing Multivariate Fekete and Leja
Points by Numerical Linear Algebra . . . 1984--1999
M. Asadzadeh and
A. H. Schatz and
W. Wendland Asymptotic Error Expansions for the
Finite Element Method for Second Order
Elliptic Problems in $ R^N $, $ N \geq 2
$. I: Local Interior Expansions . . . . 2000--2017
Erik Burman and
Alexandre Ern and
Miguel A. Fernández Explicit Runge--Kutta Schemes and Finite
Elements with Symmetric Stabilization
for First-Order Linear PDE Systems . . . 2019--2042
Thorsten Hüls Computing Sacker--Sell spectra in
Discrete Time Dynamical Systems . . . . 2043--2064
Q. T. Le Gia and
I. H. Sloan and
H. Wendland Multiscale Analysis in Sobolev Spaces on
the Sphere . . . . . . . . . . . . . . . 2065--2090
Luca Gerardo-Giorda and
Fabio Nobile and
Christian Vergara Analysis and Optimization of Robin-Robin
Partitioned Procedures in
Fluid-Structure Interaction Problems . . 2091--2116
Do Y. Kwak and
Kye T. Wee and
Kwang S. Chang An Analysis of a Broken $ P_1
$-Nonconforming Finite Element Method
for Interface Problems . . . . . . . . . 2117--2134
Congpei An and
Xiaojun Chen and
Ian H. Sloan and
Robert S. Womersley Well Conditioned Spherical Designs for
Integration and Interpolation on the
Two-Sphere . . . . . . . . . . . . . . . 2135--2157
Zhiming Chen and
Weiying Zheng Convergence of the Uniaxial Perfectly
Matched Layer Method for Time-Harmonic
Scattering Problems in Two-Layered Media 2158--2185
Xiaobing Feng and
Yinnian He Fully Discrete Finite Element
Approximations of a Polymer Gel Model 2186--2217
R. Eymard and
T. Gallouët and
R. Herbin and
J.-C. Latché Convergence of the MAC Scheme for the
Compressible Stokes Equations . . . . . 2218--2246
François Bouchon and
Gunther H. Peichl The Immersed Interface Technique for
Parabolic Problems with Mixed Boundary
Conditions . . . . . . . . . . . . . . . 2247--2266
Weidong Chen Computation of Fourier Transforms for
Noisy Bandlimited Signals . . . . . . . 1--14
Martin Lenz and
Simplice Firmin Nemadjieu and
Martin Rumpf A Convergent Finite Volume Scheme for
Diffusion on Evolving Surfaces . . . . . 15--37
Adrien Loseille and
Frédéric Alauzet Continuous Mesh Framework Part I:
Well-Posed Continuous Interpolation
Error . . . . . . . . . . . . . . . . . 38--60
Adrien Loseille and
Frédéric Alauzet Continuous Mesh Framework Part II:
Validations and Applications . . . . . . 61--86
Garth N. Wells Analysis of an Interface Stabilized
Finite Element Method: The
Advection--Diffusion-Reaction Equation 87--109
Sören Bartels and
Rüdiger Müller and
Christoph Ortner Robust a Priori and a Posteriori Error
Analysis for the Approximation of
Allen--Cahn and Ginzburg--Landau
Equations Past Topological Changes . . . 110--134
Daniele Boffi and
Martin Costabel and
Monique Dauge and
Leszek Demkowicz and
Ralf Hiptmair Discrete Compactness for the $p$-Version
of Discrete Differential Forms . . . . . 135--158
Pavel B. Bochev and
Kara Peterson and
Christopher M. Siefert Analysis and Computation of Compatible
Least-Squares Methods for div-curl
Equations . . . . . . . . . . . . . . . 159--181
Nabi Chegini and
Rob Stevenson Adaptive Wavelet Schemes for Parabolic
Problems: Sparse Matrices and Numerical
Results . . . . . . . . . . . . . . . . 182--212
J. H. Witte and
C. Reisinger A Penalty Method for the Numerical
Solution of Hamilton--Jacobi--Bellman
(HJB) Equations in Finance . . . . . . . 213--231
R. I. McLachlan and
Y. Sun and
P. S. P. Tse Linear Stability of Partitioned
Runge--Kutta Methods . . . . . . . . . . 232--263
R. Hiptmair and
A. Moiola and
I. Perugia Plane Wave Discontinuous Galerkin
Methods for the $2$D Helmholtz Equation:
Analysis of the $p$-Version . . . . . . 264--284
Juho Könnö and
Dominik Schötzau and
Rolf Stenberg Mixed Finite Element Methods for
Problems with Robin Boundary Conditions 285--308
Victor Kalvin Perfectly Matched Layers for Diffraction
Gratings in Inhomogeneous Media.
Stability and Error Estimates . . . . . 309--330
Snorre H. Christiansen and
Tore G. Halvorsen A Gauge Invariant Discretization on
Simplicial Grids of the Schrödinger
Eigenvalue Problem in an Electromagnetic
Field . . . . . . . . . . . . . . . . . 331--345
Christoph Ortner and
Dirk Praetorius On the Convergence of Adaptive
Nonconforming Finite Element Methods for
a Class of Convex Variational Problems 346--367
Katharine Gurski and
Stephen O'Sullivan A Stability Study of a New Explicit
Numerical Scheme for a System of
Differential Equations with a Large
Skew-Symmetric Component . . . . . . . . 368--386
Steffen Münzenmaier and
Gerhard Starke First-Order System Least Squares for
Coupled Stokes--Darcy Flow . . . . . . . 387--404
Irene Kyza and
Charalambos Makridakis Analysis for Time Discrete
Approximations of Blow-up Solutions of
Semilinear Parabolic Equations . . . . . 405--426
Emmanuil H. Georgoulis and
Omar Lakkis and
Juha M. Virtanen A Posteriori Error Control for
Discontinuous Galerkin Methods for
Parabolic Problems . . . . . . . . . . . 427--458
Jérôme Droniou and
Christophe Le Potier Construction and Convergence Study of
Schemes Preserving the Elliptic Local
Maximum Principle . . . . . . . . . . . 459--490
Ross Ingram Finite Element Approximation of
Nonsolenoidal, Viscous Flows around
Porous and Solid Obstacles . . . . . . . 491--520
JaEun Ku Pointwise Error Estimates for
First-Order div Least-Squares Finite
Element Methods and Applications to
Superconvergence and a Posteriori Error
Estimators . . . . . . . . . . . . . . . 521--540
Yuan Xu On Gauss--Lobatto Integration on the
Triangle . . . . . . . . . . . . . . . . 541--548
Qinian Jin A General Convergence Analysis of Some
Newton-Type methods for Nonlinear
Inverse Problems . . . . . . . . . . . . 549--573
Jianguo Huang and
Xuehai Huang and
Yifeng Xu Convergence of an Adaptive Mixed Finite
Element Method for Kirchhoff Plate
Bending Problems . . . . . . . . . . . . 574--607
Hongjiong Tian and
Quanhong Yu and
Jiaoxun Kuang Asymptotic Stability of Linear Neutral
Delay Differential-Algebraic Equations
and Linear Multistep Methods . . . . . . 608--618
Weifeng Qiu and
Leszek Demkowicz Mixed hp-Finite Element Method for
Linear Elasticity with Weakly Imposed
Symmetry: Stability Analysis . . . . . . 619--641
Arnulf Jentzen Higher Order Pathwise Numerical
Approximations of SPDEs with Additive
Noise . . . . . . . . . . . . . . . . . 642--667
Young-Ju Lee and
Hengguang Li On Stability, Accuracy, and Fast Solvers
for Finite Element Approximations of the
Axisymmetric Stokes Problem by
Hood--Taylor Elements . . . . . . . . . 668--691
C. Wieners and
B. Wohlmuth A Primal-Dual Finite Element
Approximation for a Nonlocal Model in
Plasticity . . . . . . . . . . . . . . . 692--710
Hyesuk K. Lee and
Maxim A. Olshanskii and
Leo G. Rebholz On Error Analysis for the $3$D
Navier--Stokes Equations in
Velocity-Vorticity-Helicity Form . . . . 711--732
Hao Wu and
Xu Yang A Hybrid Phase Flow Method for Solving
the Liouville Equation in a Bounded
Domain . . . . . . . . . . . . . . . . . 733--754
JaEun Ku Sharp $ L_2 $-Norm Error Estimates for
First-Order div Least-Squares Methods 755--769
Michele Benzi and
Maxim A. Olshanskii Field-of-Values Convergence Analysis of
Augmented Lagrangian Preconditioners for
the Linearized Navier--Stokes Problem 770--788
Edwin M. Behrens and
Johnny Guzmán A Mixed Method for the Biharmonic
Problem Based On a System of First-Order
Equations . . . . . . . . . . . . . . . 789--817
A. Buffa and
J. Rivas and
G. Sangalli and
R. Vázquez Isogeometric Discrete Differential Forms
in Three Dimensions . . . . . . . . . . 818--844
Jingyue Wang and
Bradley J. Lucier Error Bounds for Finite-Difference
Methods for Rudin--Osher--Fatemi Image
Smoothing . . . . . . . . . . . . . . . 845--868
Susanne C. Brenner and
Michael Neilan A $ \mathcal {C}^0 $ Interior Penalty
Method for a Fourth Order Elliptic
Singular Perturbation Problem . . . . . 869--892
F. Ar\`andiga and
A. Baeza and
A. M. Belda and
P. Mulet Analysis of WENO Schemes for Full and
Global Accuracy . . . . . . . . . . . . 893--915
J.-L. Guermond and
Abner J. Salgado Error Analysis of a Fractional
Time-Stepping Technique for
Incompressible Flows with Variable
Density . . . . . . . . . . . . . . . . 917--944
C. Wang and
S. M. Wise An Energy Stable and Convergent
Finite-Difference Scheme for the
Modified Phase Field Crystal Equation 945--969
Roland Becker and
Shipeng Mao Quasi-Optimality of Adaptive
Nonconforming Finite Element Methods for
the Stokes Equations . . . . . . . . . . 970--991
Thomas Apel and
Olaf Benedix and
Dieter Sirch and
Boris Vexler A Priori Mesh Grading for an Elliptic
Problem with Dirac Right-Hand Side . . . 992--1005
Gerhard Starke and
Alexander Schwarz and
Jörg Schröder Analysis of a Modified First-Order
System Least Squares Method for Linear
Elasticity with Improved Momentum
Balance . . . . . . . . . . . . . . . . 1006--1022
Siddhartha Mishra and
Eitan Tadmor Constraint Preserving Schemes Using
Potential-Based Fluxes. II. Genuinely
Multidimensional Systems of Conservation
Laws . . . . . . . . . . . . . . . . . . 1023--1045
A. H. Barnett and
A. Hassell Boundary Quasi-Orthogonality and Sharp
Inclusion Bounds for Large Dirichlet
Eigenvalues . . . . . . . . . . . . . . 1046--1063
Wenbin Chen and
Max Gunzburger and
Fei Hua and
Xiaoming Wang A Parallel Robin--Robin Domain
Decomposition Method for the
Stokes--Darcy System . . . . . . . . . . 1064--1084
Beatrice M. Rivi\`ere and
Noel J. Walkington Convergence of a Discontinuous Galerkin
Method for the Miscible Displacement
Equation under Low Regularity . . . . . 1085--1110
Brian A. Hagler Optimizing Gaussian Quadrature for
Positive Definite Strong Moment
Functionals . . . . . . . . . . . . . . 1111--1126
Victor D. Didenko and
Johan Helsing Stability of the Nyström Method for the
Sherman--Lauricella Equation . . . . . . 1127--1148
Volker John and
Julia Novo Error Analysis of the SUPG Finite
Element Discretization of Evolutionary
Convection--Diffusion-Reaction Equations 1149--1176
Habib Ammari and
Hyeonbae Kang and
Eunjoo Kim and
Mikyoung Lim and
Kaouthar Louati A Direct Algorithm for Ultrasound
Imaging of Internal Corrosion . . . . . 1177--1193
Nicola Guglielmi and
Christian Lubich Differential Equations for Roaming
Pseudospectra: Paths to Extremal Points
and Boundary Tracking . . . . . . . . . 1194--1209
J. M. Melenk and
S. Sauter Wavenumber Explicit Convergence Analysis
for Galerkin Discretizations of the
Helmholtz Equation . . . . . . . . . . . 1210--1243
I. C. F. Ipsen and
C. T. Kelley and
S. R. Pope Rank-Deficient Nonlinear Least Squares
Problems and Subset Selection . . . . . 1244--1266
L. Formaggia and
A. Scotti Positivity and Conservation Properties
of Some Integration Schemes for Mass
Action Kinetics . . . . . . . . . . . . 1267--1288
Felix Kwok Optimized Additive Schwarz with Harmonic
Extension as a Discretization of the
Continuous Parallel Schwarz Method . . . 1289--1316
Miodrag S. Petkovi\'c Remarks on ``On a General Class of
Multipoint Root-Finding Methods of High
Computational Efficiency'' . . . . . . . 1317--1319
Eunjung Lee and
Max Gunzburger Analysis of Finite Element
Discretizations of an Optimal Control
Formulation of the Image Registration
Problem . . . . . . . . . . . . . . . . 1321--1349
Jun Hu and
Yunqing Huang and
Shangyou Zhang The Lowest Order Differentiable Finite
Element on Rectangular Grids . . . . . . 1350--1368
K. Mustapha and
H. Brunner and
H. Mustapha and
D. Schötzau An $ h p$-Version Discontinuous Galerkin
Method for Integro-Differential
Equations of Parabolic Type . . . . . . 1369--1396
Andrei Yevik and
Huaizhong Zhao Numerical Approximations to the
Stationary Solutions of Stochastic
Differential Equations . . . . . . . . . 1397--1416
Pei Chen Hessian Matrix vs. Gauss--Newton Hessian
Matrix . . . . . . . . . . . . . . . . . 1417--1435
Anton Arnold and
Naoufel Ben Abdallah and
Claudia Negulescu WKB-Based Schemes for the Oscillatory
$1$D Schrödinger Equation in the
Semiclassical Limit . . . . . . . . . . 1436--1460
Michael A. Case and
Vincent J. Ervin and
Alexander Linke and
Leo G. Rebholz A Connection Between Scott--Vogelius and
Grad-Div Stabilized Taylor--Hood FE
Approximations of the Navier--Stokes
Equations . . . . . . . . . . . . . . . 1461--1481
Joachim Schöberl and
René Simon and
Walter Zulehner A Robust Multigrid Method for Elliptic
Optimal Control Problems . . . . . . . . 1482--1503
J. Gopalakrishnan and
J. Guzmán Symmetric Nonconforming Mixed Finite
Elements for Linear Elasticity . . . . . 1504--1520
O. Steinbach A Note on the Stable One-Equation
Coupling of Finite and Boundary Elements 1521--1531
Max D. Gunzburger and
Hyung-Chun Lee and
Jangwoon Lee Error Estimates of Stochastic Optimal
Neumann Boundary Control Problems . . . 1532--1552
Charles B. Harris and
Richard D. Noren Uniform $ l^1 $ Behavior of a Time
Discretization Method for a Volterra
Integrodifferential Equation with Convex
Kernel; Stability . . . . . . . . . . . 1553--1571
T. Betcke and
E. A. Spence Numerical Estimation of Coercivity
Constants for Boundary Integral
Operators in Acoustic Scattering . . . . 1572--1601
Yidu Yang and
Hai Bi Two-Grid Finite Element Discretization
Schemes Based on Shifted-Inverse Power
Method for Elliptic Eigenvalue Problems 1602--1624
Yanping Chen and
Fenglin Huang and
Nianyu Yi and
Wenbin Liu A Legendre--Galerkin Spectral Method for
Optimal Control Problems Governed by
Stokes Equations . . . . . . . . . . . . 1625--1648
David I. Ketcheson Step Sizes for Strong Stability
Preservation with Downwind-Biased
Operators . . . . . . . . . . . . . . . 1649--1660
Josef Dick Quasi-Monte Carlo Numerical Integration
on $ \mathbb {R}^s $: Digital Nets and
Worst-Case Error . . . . . . . . . . . . 1661--1691
Brittany D. Froese and
Adam M. Oberman Convergent Finite Difference Solvers for
Viscosity Solutions of the Elliptic
Monge--Amp\`ere Equation in Dimensions
Two and Higher . . . . . . . . . . . . . 1692--1714
Homer F. Walker and
Peng Ni Anderson Acceleration for Fixed-Point
Iterations . . . . . . . . . . . . . . . 1715--1735
L. Beirão da Veiga and
K. Lipnikov and
G. Manzini Arbitrary-Order Nodal Mimetic
Discretizations of Elliptic Problems on
Polygonal Meshes . . . . . . . . . . . . 1737--1760
Zhiqiang Cai and
Xiu Ye and
Shun Zhang Discontinuous Galerkin Finite Element
Methods for Interface Problems: a Priori
and a Posteriori Error Estimations . . . 1761--1787
L. Demkowicz and
J. Gopalakrishnan Analysis of the DPG Method for the
Poisson Equation . . . . . . . . . . . . 1788--1809
Vu Hoang Linh and
Volker Mehrmann Approximation of Spectral Intervals and
Leading Directions for
Differential-Algebraic Equation via
Smooth Singular Value Decompositions . . 1810--1835
J. Breidt and
T. Butler and
D. Estep A Measure-Theoretic Computational Method
for Inverse Sensitivity Problems I:
Method and Analysis . . . . . . . . . . 1836--1859
Jiguang Sun Iterative Methods for Transmission
Eigenvalues . . . . . . . . . . . . . . 1860--1874
V. Druskin and
L. Knizhnerman and
V. Simoncini Analysis of the Rational Krylov Subspace
and ADI Methods for Solving the Lyapunov
Equation . . . . . . . . . . . . . . . . 1875--1898
Hanieh Mirzaee and
Liangyue Ji and
Jennifer K. Ryan and
Robert M. Kirby Smoothness-Increasing
Accuracy-Conserving (SIAC)
Postprocessing for Discontinuous
Galerkin Solutions over Structured
Triangular Meshes . . . . . . . . . . . 1899--1920
Bin Han and
Gitta Kutyniok and
Zuowei Shen Adaptive Multiresolution Analysis
Structures and Shearlet Systems . . . . 1921--1946
Fang Liu and
Martin Stynes and
Aihui Zhou Postprocessed Two-Scale Finite Element
Discretizations, Part I . . . . . . . . 1947--1971
G. H. Zheng and
T. Wei A New Regularization Method for the Time
Fractional Inverse Advection-Dispersion
Problem . . . . . . . . . . . . . . . . 1972--1990
Martin Hanke Locating Several Small Inclusions in
Impedance Tomography from Backscatter
Data . . . . . . . . . . . . . . . . . . 1991--2016
Jialin Hong and
Shuxing Zhai and
Jingjing Zhang Discrete Gradient Approach to Stochastic
Differential Equations with a Conserved
Quantity . . . . . . . . . . . . . . . . 2017--2038
David Doyen and
Alexandre Ern Analysis of the Modified Mass Method for
the Dynamic Signorini Problem with
Coulomb Friction . . . . . . . . . . . . 2039--2056
Giacomo Dimarco and
Lorenzo Pareschi Exponential Runge--Kutta Methods for
Stiff Kinetic Equations . . . . . . . . 2057--2077
E. E. Ovtchinnikov Lehmann Bounds and Eigenvalue Error
Estimation . . . . . . . . . . . . . . . 2078--2102
Mayte Pérez-Llanos and
Julio D. Rossi Numerical Approximations for a Nonlocal
Evolution Equation . . . . . . . . . . . 2103--2123
Zvi Artstein and
C. William Gear and
Ioannis G. Kevrekidis and
Marshall Slemrod and
Edriss S. Titi Analysis and Computation of a Discrete
KdV--Burgers Type Equation with Fast
Dispersion and Slow Diffusion . . . . . 2124--2143
Igor Moret and
Paolo Novati On the Convergence of Krylov Subspace
Methods for Matrix Mittag-Leffler
Functions . . . . . . . . . . . . . . . 2144--2164
Jiangguo Liu Penalty-Factor-Free Discontinuous
Galerkin Methods for $2$-Dim Stokes
Problems . . . . . . . . . . . . . . . . 2165--2181
Brian Van Koten and
Mitchell Luskin Analysis of Energy-Based Blended
Quasi-Continuum Approximations . . . . . 2182--2209
Philsu Kim and
Xiangfan Piao and
Sang Dong Kim An Error Corrected Euler Method for
Solving Stiff Problems Based on
Chebyshev Collocation . . . . . . . . . 2211--2230
Xiangling Chen and
Zhongying Chen and
Bin Wu and
Yuesheng Xu Fast Multilevel Augmentation Methods for
Nonlinear Boundary Integral Equations 2231--2255
Timothy A. Lucas Maximum-Norm Estimates for an Immunology
Model Using Reaction-Diffusion Equations
with Stochastic Source Terms . . . . . . 2256--2276
Marcel Bieri A Sparse Composite Collocation Finite
Element Method for Elliptic SPDEs . . . 2277--2301
Ya-nan Zhang and
Zhi-zhong Sun and
Hong-wei Wu Error Estimates of Crank--Nicolson-Type
Difference Schemes for the Subdiffusion
Equation . . . . . . . . . . . . . . . . 2302--2322
Andreas Schröder Mixed Finite Element Methods of
Higher-Order for Model Contact Problems 2323--2339
Maike Löhndorf and
Jens Markus Melenk Wavenumber-Explicit $ h p$-BEM for High
Frequency Scattering . . . . . . . . . . 2340--2363
Kwang-Yeon Kim Guaranteed a Posteriori Error Estimator
for Mixed Finite Element Methods of
Linear Elasticity with Weak Stress
Symmetry . . . . . . . . . . . . . . . . 2364--2385
Jiequan Li and
Zhicheng Yang Heuristic Modified Equation Analysis on
Oscillations in Numerical Solutions of
Conservation Laws . . . . . . . . . . . 2386--2406
Mihály Kovács and
Stig Larsson and
Ali Mesforush Finite Element Approximation of the
Cahn--Hilliard--Cook Equation . . . . . 2407--2429
Bernhard Beckermann An Error Analysis for Rational Galerkin
Projection Applied to the Sylvester
Equation . . . . . . . . . . . . . . . . 2430--2450
Roland Becker and
Elodie Estecahandy and
David Trujillo Weighted Marking for Goal-oriented
Adaptive Finite Element Methods . . . . 2451--2469
Elisabetta Carlini and
Nicolas Forcadel and
Régis Monneau A Generalized Fast Marching Method for
Dislocation Dynamics . . . . . . . . . . 2470--2500
Carsten Carstensen and
Dongho Kim and
Eun-Jae Park A Priori and a Posteriori
Pseudostress-velocity Mixed Finite
Element Error Analysis for the Stokes
Problem . . . . . . . . . . . . . . . . 2501--2523
M. Dashti and
A. M. Stuart Uncertainty Quantification and Weak
Approximation of an Elliptic Inverse
Problem . . . . . . . . . . . . . . . . 2524--2542
Simon Foucart Hard Thresholding Pursuit: An Algorithm
for Compressive Sensing . . . . . . . . 2543--2563
Zhiqiang Cai and
JaEun Ku Goal-Oriented Local a Posteriori Error
Estimators for $H$(div) Least-Squares
Finite Element Methods . . . . . . . . . 2564--2575
Heiko Berninger and
Ralf Kornhuber and
Oliver Sander Fast and Robust Numerical Solution of
the Richards Equation in Homogeneous
Soil . . . . . . . . . . . . . . . . . . 2576--2597
YongHoon Kwon and
Younhee Lee A Second-order Finite Difference Method
for Option Pricing Under Jump-diffusion
Models . . . . . . . . . . . . . . . . . 2598--2617
David I. Ketcheson and
Sigal Gottlieb and
Colin B. Macdonald Strong Stability Preserving Two-step
Runge--Kutta Methods . . . . . . . . . . 2618--2639
Alina Chertock and
Jian-Guo Liu and
Terrance Pendleton Convergence of a Particle Method and
Global Weak Solutions of a Family of
Evolutionary PDEs . . . . . . . . . . . 1--21
T. Butler and
D. Estep and
J. Sandelin A Computational Measure Theoretic
Approach to Inverse Sensitivity Problems
II: a Posteriori Error Analysis . . . . 22--45
Saifon Chaturantabut and
Danny C. Sorensen A State Space Error Estimate for
POD--DEIM Nonlinear Model Reduction . . 46--63
Mathew A. Johnson and
Kevin Zumbrun Convergence of Hill's Method for
Nonselfadjoint Operators . . . . . . . . 64--78
Yan Xu and
Chi-Wang Shu Optimal Error Estimates of the
Semidiscrete Local Discontinuous
Galerkin Methods for High Order Wave
Equations . . . . . . . . . . . . . . . 79--104
Jie Shen and
Cheng Wang and
Xiaoming Wang and
Steven M. Wise Second-order Convex Splitting Schemes
for Gradient Flows with
Ehrlich--Schwoebel Type Energy:
Application to Thin Film Epitaxy . . . . 105--125
S. Gottlieb and
F. Tone and
C. Wang and
X. Wang and
D. Wirosoetisno Long Time Stability of a Classical
Efficient Scheme for Two-dimensional
Navier--Stokes Equations . . . . . . . . 126--150
Zhiqiang Cai and
Shun Zhang Robust Equilibrated Residual Error
Estimator for Diffusion Problems:
Conforming Elements . . . . . . . . . . 151--170
Jiawei Chiu and
Laurent Demanet Matrix Probing and its Conditioning . . 171--193
Carlo D'Angelo Finite Element Approximation of Elliptic
Problems with Dirac Measure Terms in
Weighted Spaces: Applications to One-
and Three-dimensional Coupled Problems 194--215
Julia Charrier Strong and Weak Error Estimates for
Elliptic Partial Differential Equations
with Random Coefficients . . . . . . . . 216--246
Gregory E. Fasshauer and
Fred J. Hickernell and
Henryk Wo\'zniakowski On Dimension-independent Rates of
Convergence for Function Approximation
with Gaussian Kernels . . . . . . . . . 247--271
Ahmed Naga and
Zhimin Zhang Function Value Recovery and Its
Application in Eigenvalue Problems . . . 272--286
Marko Lindner and
Steffen Roch Finite Sections of Random Jacobi
Operators . . . . . . . . . . . . . . . 287--306
María José Cantero and
Arieh Iserles On Rapid Computation of Expansions in
Ultraspherical Polynomials . . . . . . . 307--327
Andrei Draganescu and
Cosmin Petra Multigrid Preconditioning of Linear
Systems for Interior Point Methods
Applied to a Class of Box-constrained
Optimal Control Problems . . . . . . . . 328--353
Nan Li and
Lihong Zhi Computing Isolated Singular Solutions of
Polynomial Systems: Case of Breadth One 354--372
L. Belenki and
L. C. Berselli and
L. Diening and
M. R\ocircu\vzi\vcka On the Finite Element Approximation of
$p$-Stokes Systems . . . . . . . . . . . 373--397
Santiago Badia and
Ramon Codina A Nodal-based Finite Element
Approximation of the Maxwell Problem
Suitable for Singular Solutions . . . . 398--417
R. Altmann and
C. Carstensen $ P_1 $-Nonconforming Finite Elements on
Triangulations into Triangles and
Quadrilaterals . . . . . . . . . . . . . 418--438
J. G. Verwer Composition Methods, Maxwell's
Equations, and Source Terms . . . . . . 439--457
P. Wojtaszczyk $ \ell_1 $ Minimization with Noisy Data 458--467
Christophe Berthon and
Bruno Dubroca and
Afeintou Sangam A Local Entropy Minimum Principle for
Deriving Entropy Preserving Schemes . . 468--491
Weizhu Bao and
Yongyong Cai Uniform Error Estimates of Finite
Difference Methods for the Nonlinear
Schrödinger Equation with Wave Operator 492--521
Carsten Carstensen and
David Günther and
Hella Rabus Mixed Finite Element Method for a
Degenerate Convex Variational Problem
from Topology Optimization . . . . . . . 522--543
Ulrik S. Fjordholm and
Siddhartha Mishra and
Eitan Tadmor Arbitrarily High-order Accurate Entropy
Stable Essentially Nonoscillatory
Schemes for Systems of Conservation Laws 544--573
Christoph Erath Coupling of the Finite Volume Element
Method and the Boundary Element Method:
An a Priori Convergence Result . . . . . 574--594
J. H. Witte and
C. Reisinger Penalty Methods for the Solution of
Discrete HJB Equations-Continuous
Control and Obstacle Problems . . . . . 595--625
Junping Wang and
Ran Zhang Maximum Principles for $ P1 $-Conforming
Finite Element Approximations of
Quasi-linear Second Order Elliptic
Equations . . . . . . . . . . . . . . . 626--642
Georges Klein and
Jean-Paul Berrut Linear Rational Finite Differences from
Derivatives of Barycentric Rational
Interpolants . . . . . . . . . . . . . . 643--656
Thirupathi Gudi Finite Element Method for a Nonlocal
Problem of Kirchhoff Type . . . . . . . 657--668
Rodolfo Araya and
Gabriel R. Barrenechea and
Abner H. Poza and
Frédéric Valentin Convergence Analysis of a Residual Local
Projection Finite Element Method for the
Navier--Stokes Equations . . . . . . . . 669--699
Bingsheng He and
Xiaoming Yuan On the $ O(1 / n) $ Convergence Rate of
the Douglas--Rachford Alternating
Direction Method . . . . . . . . . . . . 700--709
O. Steinbach and
G. Unger Convergence Analysis of a Galerkin
Boundary Element Method for the
Dirichlet Laplacian Eigenvalue Problem 710--728
Philipp Dörsek Semigroup Splitting and Cubature
Approximations for the Stochastic
Navier--Stokes Equations . . . . . . . . 729--746
Gilles Pag\`es and
Benedikt Wilbertz Intrinsic Stationarity for Vector
Quantization: Foundation of Dual
Quantization . . . . . . . . . . . . . . 747--780
Michael Gnewuch and
Magnus Wahlström and
Carola Winzen A New Randomized Algorithm to
Approximate the Star Discrepancy Based
on Threshold Accepting . . . . . . . . . 781--807
Stella Krell and
Gianmarco Manzini The Discrete Duality Finite Volume
Method for Stokes Equations on
Three-Dimensional Polyhedral Meshes . . 808--837
Daniela Schräder and
Holger Wendland An Extended Error Analysis for a
Meshfree Discretization Method of
Darcy's Problem . . . . . . . . . . . . 838--857
Marta Benítez and
Alfredo Bermúdez Numerical Analysis of a Second order
Pure Lagrange--Galerkin Method for
Convection--Diffusion Problems. Part I:
Time Discretization . . . . . . . . . . 858--882
R. Natalini and
M. Ribot Asymptotic High Order Mass-Preserving
Schemes for a Hyperbolic Model of
Chemotaxis . . . . . . . . . . . . . . . 883--905
JaEun Ku and
Alfred H. Schatz Local a Posteriori Estimates on a
Nonconvex Polygonal Domain . . . . . . . 906--924
M. Doumic and
M. Hoffmann and
P. Reynaud-Bouret and
V. Rivoirard Nonparametric Estimation of the Division
Rate of a Size-Structured Population . . 925--950
Sören Bartels and
Alexander Mielke and
Tomás Roubícek Quasi-Static Small-Strain Plasticity in
the Limit of Vanishing Hardening and Its
Numerical Approximation . . . . . . . . 951--976
Nicola Guglielmi and
Christian Lubich Erratum/Addendum: Differential Equations
for Roaming Pseudospectra: Paths to
Extremal Points and Boundary Tracking 977--981
Jianping Zhang and
Ke Chen and
Bo Yu An Iterative Lagrange Multiplier Method
for Constrained Total-Variation-Based
Image Denoising . . . . . . . . . . . . 983--1003
Clark R. Dohrmann and
Olof B. Widlund An Iterative Substructuring Algorithm
for Two-Dimensional Problems in
$H$(curl) . . . . . . . . . . . . . . . 1004--1028
Carsten Carstensen and
Joscha Gedicke An Adaptive Finite Element Eigenvalue
Solver of Asymptotic Quasi-Optimal
Computational Complexity . . . . . . . . 1029--1057
Erwan Deriaz Stability Conditions for the Numerical
Solution of Convection-Dominated
Problems with Skew-Symmetric
Discretizations . . . . . . . . . . . . 1058--1085
Ivan Cimrák Material and Shape Derivative Method for
Quasi-Linear Elliptic Systems with
Applications in Inverse Electromagnetic
Interface Problems . . . . . . . . . . . 1086--1110
Giovanni Russo and
Pietro Santagati and
Seok-Bae Yun Convergence of a Semi-Lagrangian Scheme
for the BGK Model of the Boltzmann
Equation . . . . . . . . . . . . . . . . 1111--1135
Jie Shen and
Haijun Yu On the Approximation of the
Fokker--Planck Equation of the Finitely
Extensible Nonlinear Elastic Dumbbell
Model I: a New Weighted Formulation and
an Optimal Spectral-Galerkin Algorithm
in Two Dimensions . . . . . . . . . . . 1136--1161
Sören Bartels Total Variation Minimization with Finite
Elements: Convergence and Iterative
Solution . . . . . . . . . . . . . . . . 1162--1180
Jan Cesenek and
Miloslav Feistauer Theory of the Space--time Discontinuous
Galerkin Method for Nonstationary
Parabolic Problems with Nonlinear
Convection and Diffusion . . . . . . . . 1181--1206
Hailiang Liu and
Hui Yu An Entropy Satisfying Conservative
Method for the Fokker--Planck Equation
of the Finitely Extensible Nonlinear
Elastic Dumbbell Model . . . . . . . . . 1207--1239
Shuhuang Xiang On Error Bounds for Orthogonal
Polynomial Expansions and Gauss-Type
Quadrature . . . . . . . . . . . . . . . 1240--1263
Carsten Carstensen and
Hella Rabus The Adaptive Nonconforming FEM for the
Pure Displacement Problem in Linear
Elasticity is Optimal and Robust . . . . 1264--1283
Adérito Araújo and
Sílvia Barbeiro and
Pedro Serranho Stability of Finite Difference Schemes
for Complex Diffusion Processes . . . . 1284--1296
Jeffrey M. Connors and
Jason S. Howell and
William J. Layton Decoupled Time Stepping Methods for
Fluid-Fluid Interaction . . . . . . . . 1297--1319
Xiaobing Feng and
Steven Wise Analysis of a Darcy--Cahn--Hilliard
Diffuse Interface Model for the
Hele--Shaw Flow and Its Fully Discrete
Finite Element Approximation . . . . . . 1320--1343
A. Bompadre and
B. Schmidt and
M. Ortiz Convergence Analysis of Meshfree
Approximation Schemes . . . . . . . . . 1344--1366
Sajid Memon and
Neela Nataraj and
Amiya Kumar Pani An a Posteriori Error Analysis of Mixed
Finite Element Galerkin Approximations
to Second Order Linear Parabolic
Problems . . . . . . . . . . . . . . . . 1367--1393
L. Beiraño da Veiga and
D. Cho and
L. F. Pavarino and
S. Scacchi Overlapping Schwarz Methods for
Isogeometric Analysis . . . . . . . . . 1394--1416
Bernardo Cockburn and
Weifeng Qiu and
Ke Shi Superconvergent HDG Methods on
Isoparametric Elements for Second-Order
Elliptic Problems . . . . . . . . . . . 1417--1432
Alexey Chernov and
Christoph Schwab Exponential Convergence of Gauss--Jacobi
Quadratures for Singular Integrals over
Simplices in Arbitrary Dimension . . . . 1433--1455
D. Breda and
S. Maset and
R. Vermiglio Approximation of Eigenvalues of
Evolution Operators for Linear Retarded
Functional Differential Equations . . . 1456--1483
Thomas Apel and
Thomas G. Flaig Crank--Nicolson Schemes for Optimal
Control Problems with Evolution
Equations . . . . . . . . . . . . . . . 1484--1512
Congpei An and
Xiaojun Chen and
Ian H. Sloan and
Robert S. Womersley Regularized Least Squares Approximations
on the Sphere Using Spherical Designs 1513--1534
Ya-nan Zhang and
Zhi-zhong Sun and
Xuan Zhao Compact Alternating Direction Implicit
Scheme for the Two-Dimensional
Fractional Diffusion-Wave Equation . . . 1535--1555
Heinz-Otto Kreiss and
N. Anders Petersson Boundary Estimates for the Elastic Wave
Equation in Almost Incompressible
Materials . . . . . . . . . . . . . . . 1556--1580
O. Bruno and
D. Hoch Numerical Differentiation of
Approximated Functions with Limited
Order-of-Accuracy Deterioration . . . . 1581--1603
Tymofiy Gerasimov and
Athanasios Stylianou and
Guido Sweers Corners Give Problems When Decoupling
Fourth Order Equations Into Second Order
Systems . . . . . . . . . . . . . . . . 1604--1623
Alan Demlow and
Maxim A. Olshanskii An Adaptive Surface Finite Element
Method Based on Volume Meshes . . . . . 1624--1647
Gabriel N. Gatica and
Antonio Márquez and
Salim Meddahi Analysis of the Coupling of Lagrange and
Arnold--Falk--Winther Finite Elements
for a Fluid-Solid Interaction Problem in
Three Dimensions . . . . . . . . . . . . 1648--1674
Robert Scheichl and
Panayot S. Vassilevski and
Ludmil T. Zikatanov Multilevel Methods for Elliptic Problems
with Highly Varying Coefficients on
Nonaligned Coarse Grids . . . . . . . . 1675--1694
Laslo T. Diosady and
David L. Darmofal A Unified Analysis of Balancing Domain
Decomposition by Constraints for
Discontinuous Galerkin Discretizations 1695--1712
Ricardo Pachón and
Pedro Gonnet and
Joris van Deun Fast and Stable Rational Interpolation
in Roots of Unity and Chebyshev Points 1713--1734
Arnaud Debussche and
Erwan Faou Weak Backward Error Analysis for SDEs 1735--1752
Edward Fuselier and
Grady B. Wright Scattered Data Interpolation on Embedded
Submanifolds with Restricted Positive
Definite Kernels: Sobolev Error
Estimates . . . . . . . . . . . . . . . 1753--1776
Stefan Kunis and
Ines Melzer A Stable and Accurate Butterfly Sparse
Fourier Transform . . . . . . . . . . . 1777--1800
Tan Bui-Thanh and
Omar Ghattas Analysis of an $ h p$-Nonconforming
Discontinuous Galerkin Spectral Element
Method for Wave Propagation . . . . . . 1801--1826
Martin Berggren and
Fotios Kasolis Weak Material Approximation of Holes
with Traction-Free Boundaries . . . . . 1827--1848
Michelle Ghrist and
Bengt Fornberg Two Results Concerning the Stability of
Staggered Multistep Methods . . . . . . 1849--1860
Y. Huang and
P. A. Forsyth and
G. Labahn Combined Fixed Point and Policy
Iteration for Hamilton--Jacobi--Bellman
Equations in Finance . . . . . . . . . . 1861--1882
Andrea Braides and
Nung Kwan Yip A Quantitative Description of Mesh
Dependence for the Discretization of
Singularly Perturbed Nonconvex Problems 1883--1898
Jingyan Zhang and
Qiang Du Shrinking Dimer Dynamics and Its
Applications to Saddle Point Search . . 1899--1921
Guannan Zhang and
Max Gunzburger Error Analysis of a Stochastic
Collocation Method for Parabolic Partial
Differential Equations with Random Input
Data . . . . . . . . . . . . . . . . . . 1922--1940
Do Y. Kwak A New Class of Higher Order Mixed Finite
Volume Methods for Elliptic Problems . . 1941--1958
Erik Burman A Penalty-Free Nonsymmetric Nitsche-Type
Method for the Weak Imposition of
Boundary Conditions . . . . . . . . . . 1959--1981
Jinhai Chen and
Matthias Gerdts Smoothing Technique of Nonsmooth Newton
Methods for Control-State Constrained
Optimal Control Problems . . . . . . . . 1982--2011
Dmitriy Leykekhman and
Matthias Heinkenschloss Local Error Analysis of Discontinuous
Galerkin Methods for Advection-Dominated
Elliptic Linear-Quadratic Optimal
Control Problems . . . . . . . . . . . . 2012--2038
Alexei Bespalov and
Catherine E. Powell and
David Silvester A Priori Error Analysis of Stochastic
Galerkin Mixed Approximations of
Elliptic PDEs with Random Data . . . . . 2039--2063
J. M. Melenk and
B. Wohlmuth Quasi-Optimal Approximation of Surface
Based Lagrange Multipliers in Finite
Element Methods . . . . . . . . . . . . 2064--2087
Susanne C. Brenner and
Shiyuan Gu and
Thirupathi Gudi and
Li-yeng Sung A Quadratic $ C^0 $ Interior Penalty
Method for Linear Fourth Order Boundary
Value Problems with Boundary Conditions
of the Cahn--Hilliard Type . . . . . . . 2088--2110
Martin J. Gander and
Ronald D. Haynes Domain Decomposition Approaches for Mesh
Generation via the Equidistribution
Principle . . . . . . . . . . . . . . . 2111--2135
Philippe G. LeFloch and
Hasan Makhlof and
Baver Okutmustur Relativistic Burgers Equations on Curved
Spacetimes. Derivation and Finite Volume
Approximation . . . . . . . . . . . . . 2136--2158
Alan Demlow and
Emmanuil H. Georgoulis Pointwise a Posteriori Error Control for
Discontinuous Galerkin Methods for
Elliptic Problems . . . . . . . . . . . 2159--2181
Bernhard A. Schmitt and
Ekaterina Kostina Peer Two-Step Methods with Embedded
Sensitivity Approximation for
Parameter-Dependent ODEs . . . . . . . . 2182--2207
Sabrina Gippert and
Axel Klawonn and
Oliver Rheinbach Analysis of FETI-DP and BDDC for Linear
Elasticity in $3$D with Almost
Incompressible Components and Varying
Coefficients Inside Subdomains . . . . . 2208--2236
David F. Anderson An Efficient Finite Difference Method
for Parameter Sensitivities of
Continuous Time Markov Chains . . . . . 2237--2258
Habib Ammari and
Elie Bretin and
Josselin Garnier and
Vincent Jugnon Coherent Interferometry Algorithms for
Photoacoustic Imaging . . . . . . . . . 2259--2280
Eduardo Casas and
Konstantinos Chrysafinos A Discontinuous Galerkin Time-Stepping
Scheme for the Velocity Tracking Problem 2281--2306
Vincent J. Ervin and
William J. Layton and
Monika Neda Numerical Analysis of Filter-Based
Stabilization for Evolution Equations 2307--2335
Xiong Meng and
Chi-Wang Shu and
Qiang Zhang and
Boying Wu Superconvergence of Discontinuous
Galerkin Methods for Scalar Nonlinear
Conservation Laws in One Space Dimension 2336--2356
Sergej Rjasanow and
Steffen Weißer Higher Order BEM-Based FEM on Polygonal
Meshes . . . . . . . . . . . . . . . . . 2357--2378
Junliang Lv and
Yonghai Li Optimal Biquadratic Finite Volume
Element Methods on Quadrilateral Meshes 2379--2399
Patrick Hild and
Yves Renard An Improved a Priori Error Analysis for
Finite Element Approximations of
Signorini's Problem . . . . . . . . . . 2400--2419
Wolfgang Dahmen and
Chunyan Huang and
Christoph Schwab and
Gerrit Welper Adaptive Petrov--Galerkin Methods for
First Order Transport Equations . . . . 2420--2445
Ming-Jun Lai and
Leopold Matamba Messi Piecewise Linear Approximation of the
Continuous Rudin--Osher--Fatemi Model
for Image Denoising . . . . . . . . . . 2446--2466
Erich Carelli and
Andreas Prohl Rates of Convergence for Discretizations
of the Stochastic Incompressible
Navier--Stokes Equations . . . . . . . . 2467--2496
Leandro M. Del Pezzo and
Ariel L. Lombardi and
Sandra Martínez Interior Penalty Discontinuous Galerkin
FEM for the $ p(x) $-Laplacian . . . . . 2497--2521
Clark R. Dohrmann and
Olof B. Widlund An Alternative Coarse Space for
Irregular Subdomains and an Overlapping
Schwarz Algorithm for Scalar Elliptic
Problems in the Plane . . . . . . . . . 2522--2537
Alexander Rand Average Interpolation under the Maximum
Angle Condition . . . . . . . . . . . . 2538--2559
Stefan Güttel and
Georges Klein Convergence of Linear Barycentric
Rational Interpolation for Analytic
Functions . . . . . . . . . . . . . . . 2560--2580
Shuhuang Xiang and
Folkmar Bornemann On the Convergence Rates of Gauss and
Clenshaw--Curtis Quadrature for
Functions of Limited Regularity . . . . 2581--2587
Laurence Halpern and
Caroline Japhet and
Jérémie Szeftel Optimized Schwarz Waveform Relaxation
and Discontinuous Galerkin Time Stepping
for Heterogeneous Problems . . . . . . . 2588--2611
Hongxing Rui and
Hao Pan A Block-Centered Finite Difference
Method for the Darcy--Forchheimer Model 2612--2631
Zhiming Chen and
Xinming Wu Long-Time Stability and Convergence of
the Uniaxial Perfectly Matched Layer
Method for Time-Domain Acoustic
Scattering Problems . . . . . . . . . . 2632--2655
B. Haasdonk and
J. Salomon and
B. Wohlmuth A Reduced Basis Method for Parametrized
Variational Inequalities . . . . . . . . 2656--2676
Gerhard Dziuk and
Charles M. Elliott A Fully Discrete Evolving Surface Finite
Element Method . . . . . . . . . . . . . 2677--2694
Gasper Jaklic and
Jernej Kozak and
Marjeta Krajnc and
Vito Vitrih and
Emil Zagar Hermite Geometric Interpolation by
Rational Bézier Spatial Curves . . . . . 2695--2715
Masatake Hirao and
Hiroshi Nozaki and
Masanori Sawa and
Vesselin Vatchev A New Approach for the Existence Problem
of Minimal Cubature Formulas Based on
the Larman--Rogers--Seidel Theorem . . . 2716--2728
Runchang Lin and
Martin Stynes A Balanced Finite Element Method for
Singularly Perturbed Reaction-Diffusion
Problems . . . . . . . . . . . . . . . . 2729--2743
Aurora Marica and
Enrique Zuazua On the Quadratic Finite Element
Approximation of One-Dimensional Waves:
Propagation, Observation, and Control 2744--2777
Bernardo Cockburn and
Johnny Guzmán and
Francisco-Javier Sayas Coupling of Raviart--Thomas and
Hybridizable Discontinuous Galerkin
Methods with BEM . . . . . . . . . . . . 2778--2801
C. Carstensen and
D. Peterseim and
M. Schedensack Comparison Results of Finite Element
Methods for the Poisson Model Problem 2803--2823
Marta Benítez and
Alfredo Bermúdez Numerical Analysis of a Second Order
Pure Lagrange--Galerkin Method for
Convection--Diffusion Problems. Part II:
Fully Discretized Scheme and Numerical
Results . . . . . . . . . . . . . . . . 2824--2844
E. Bänsch and
F. Karakatsani and
Ch. Makridakis A Posteriori Error Control for Fully
Discrete Crank--Nicolson Schemes . . . . 2845--2872
Thomas Dunst and
Erika Hausenblas and
Andreas Prohl Approximate Euler Method for Parabolic
Stochastic Partial Differential
Equations Driven by Space--time Lévy
Noise . . . . . . . . . . . . . . . . . 2873--2896
Luigi Brugnano and
Felice Iavernaro and
Donato Trigiante Energy- and Quadratic
Invariants-Preserving Integrators Based
upon Gauss Collocation Formulae . . . . 2897--2916
Erich Carelli and
Erika Hausenblas and
Andreas Prohl Time-Splitting Methods to Solve the
Stochastic Incompressible Stokes
Equation . . . . . . . . . . . . . . . . 2917--2939
C. Ortner and
L. Zhang Construction and Sharp Consistency
Estimates for Atomistic/Continuum
Coupling Methods with General
Interfaces: a Two-Dimensional Model
Problem . . . . . . . . . . . . . . . . 2940--2965
Zhimin Zhang Superconvergence Points of Polynomial
Spectral Interpolation . . . . . . . . . 2966--2985
Yang Liu and
Yoichiro Mori Properties of Discrete Delta Functions
and Local Convergence of the Immersed
Boundary Method . . . . . . . . . . . . 2986--3015
Eric Canc\`es and
Virginie Ehrlacher and
Yvon Maday Periodic Schrödinger Operators with Local
Defects and Spectral Pollution . . . . . 3016--3035
Clément Canc\`es and
Nicolas Seguin Error Estimate for Godunov Approximation
of Locally Constrained Conservation Laws 3036--3060
Navamita Ray and
Duo Wang and
Xiangmin Jiao and
James Glimm High-Order Numerical Integration over
Discrete Surfaces . . . . . . . . . . . 3061--3083
R. Bermejo and
P. Galán del Sastre and
L. Saavedra A Second Order in Time Modified
Lagrange--Galerkin Finite Element Method
for the Incompressible Navier--Stokes
Equations . . . . . . . . . . . . . . . 3084--3109
Yang Yang and
Chi-Wang Shu Analysis of Optimal Superconvergence of
Discontinuous Galerkin Method for Linear
Hyperbolic Equations . . . . . . . . . . 3110--3133
Ralf Massjung An Unfitted Discontinuous Galerkin
Method Applied to Elliptic Interface
Problems . . . . . . . . . . . . . . . . 3134--3162
Annette F. Stephansen Convergence of the Multipoint Flux
Approximation $L$-Method on General
Grids . . . . . . . . . . . . . . . . . 3163--3187
Klaus Neymeyr A Geometric Convergence Theory for the
Preconditioned Steepest Descent
Iteration . . . . . . . . . . . . . . . 3188--3207
Huoyuan Duan and
Sha Li and
Roger C. E. Tan and
Weiying Zheng A Delta-Regularization Finite Element
Method for a Double Curl Problem with
Divergence-Free Constraint . . . . . . . 3208--3230
Mechthild Thalhammer Convergence Analysis of High-Order
Time-Splitting Pseudospectral Methods
for Nonlinear Schrödinger Equations . . . 3231--3258
Shi Jin and
Dongming Wei A Particle Method for the Semiclassical
Limit of the Schrödinger Equation and the
Vlasov--Poisson Equations . . . . . . . 3259--3279
Stefania Bellavia and
Valentina De Simone and
Daniela di Serafino and
Benedetta Morini A Preconditioning Framework for
Sequences of Diagonally Modified Linear
Systems Arising in Optimization . . . . 3280--3302
Thomas März and
Colin B. Macdonald Calculus on Surfaces with General
Closest Point Functions . . . . . . . . 3303--3328
Susanne C. Brenner and
Li-Yeng Sung and
Hongchao Zhang and
Yi Zhang A Quadratic $ C^0 $ Interior Penalty
Method for the Displacement Obstacle
Problem of Clamped Kirchhoff Plates . . 3329--3350
Frances Y. Kuo and
Christoph Schwab and
Ian H. Sloan Quasi-Monte Carlo Finite Element Methods
for a Class of Elliptic Partial
Differential Equations with Random
Coefficients . . . . . . . . . . . . . . 3351--3374
Yulia T. Peet and
Paul F. Fischer Stability Analysis of Interface Temporal
Discretization in Grid Overlapping
Methods . . . . . . . . . . . . . . . . 3375--3401
L. Beiraño da Veiga and
J. Niiranen and
R. Stenberg A Posteriori Error Analysis for the
Postprocessed MITC Plate Elements . . . 1--23
Jong Ho Lee Overlapping Domain Decomposition Methods
for Numerically Thin Reissner--Mindlin
Plates Approximated with the Falk--Tu
Elements . . . . . . . . . . . . . . . . 24--46
Eric T. Chung and
Hyea Hyun Kim and
Olof B. Widlund Two-Level Overlapping Schwarz Algorithms
for a Staggered Discontinuous Galerkin
Method . . . . . . . . . . . . . . . . . 47--67
Qiang Ye Error Bounds for the Lanczos Methods for
Approximating Matrix Exponentials . . . 68--87
Yanren Hou and
Buyang Li and
Weiwei Sun Error Estimates of Splitting Galerkin
Methods for Heat and Sweat Transport in
Textile Materials . . . . . . . . . . . 88--111
Hyoseop Lee and
Jinwoo Lee and
Dongwoo Sheen Laplace Transform Method for Parabolic
Problems with Time-Dependent
Coefficients . . . . . . . . . . . . . . 112--125
Jochen Schütz and
Sebastian Noelle and
Christina Steiner and
Georg May A Note on Adjoint Error Estimation for
One-Dimensional Stationary Balance Laws
with Shocks . . . . . . . . . . . . . . 126--136
Max Jensen and
Iain Smears On the Convergence of Finite Element
Methods for Hamilton--Jacobi--Bellman
Equations . . . . . . . . . . . . . . . 137--162
Sebastiano Boscarino and
Giovanni Russo Flux-Explicit IMEX Runge--Kutta Schemes
for Hyperbolic to Parabolic Relaxation
Problems . . . . . . . . . . . . . . . . 163--190
Alexander Ostermann and
Katharina Schratz Stability of Exponential Operator
Splitting Methods for Noncontractive
Semigroups . . . . . . . . . . . . . . . 191--203
David Cohen and
Stig Larsson and
Magdalena Sigg A Trigonometric Method for the Linear
Stochastic Wave Equation . . . . . . . . 204--222
Gary Froyland and
Oliver Junge and
Péter Koltai Estimating Long-Term Behavior of Flows
without Trajectory Integration: The
Infinitesimal Generator Approach . . . . 223--247
William Layton and
Hoang Tran and
Catalin Trenchea Analysis of Long Time Stability and
Errors of Two Partitioned Methods for
Uncoupling Evolutionary
Groundwater--Surface Water Flows . . . . 248--272
Liqun Cao and
Lei Zhang and
Walter Allegretto and
Yanping Lin Multiscale Asymptotic Method for Steklov
Eigenvalue Equations in Composite Media 273--296
Duk-Soon Oh An Overlapping Schwarz Algorithm for
Raviart--Thomas Vector Fields with
Discontinuous Coefficients . . . . . . . 297--321
J. Charrier and
R. Scheichl and
A. L. Teckentrup Finite Element Error Analysis of
Elliptic PDEs with Random Coefficients
and Its Application to Multilevel Monte
Carlo Methods . . . . . . . . . . . . . 322--352
Huiyuan Li and
Heping Ma and
Weiwei Sun Legendre Spectral Galerkin Method for
Electromagnetic Scattering from Large
Cavities . . . . . . . . . . . . . . . . 353--376
Todd Arbogast and
Hailong Xiao A Multiscale Mortar Mixed Space Based on
Homogenization for Heterogeneous
Elliptic Problems . . . . . . . . . . . 377--399
Maksymilian Dryja and
Juan Galvis and
Marcus Sarkis A FETI--DP Preconditioner for a
Composite Finite Element and
Discontinuous Galerkin Method . . . . . 400--422
Brittany D. Froese and
Adam M. Oberman Convergent Filtered Schemes for the
Monge--Amp\`ere Partial Differential
Equation . . . . . . . . . . . . . . . . 423--444
Bangti Jin and
Raytcho Lazarov and
Zhi Zhou Error Estimates for a Semidiscrete
Finite Element Method for Fractional
Order Parabolic Equations . . . . . . . 445--466
Stéphane Clain Finite Volume Maximum Principle for
Hyperbolic Scalar Problems . . . . . . . 467--490
Kassem Mustapha and
William McLean Superconvergence of a Discontinuous
Galerkin Method for Fractional Diffusion
and Wave Equations . . . . . . . . . . . 491--515
Sören Bartels Approximation of Large Bending
Isometries with Discrete Kirchhoff
Triangles . . . . . . . . . . . . . . . 516--525
Gergina V. Pencheva and
Martin Vohralík and
Mary F. Wheeler and
Tim Wildey Robust a Posteriori Error Control and
Adaptivity for Multiscale,
Multinumerics, and Mortar Coupling . . . 526--554
Anna L. Mazzucato and
Victor Nistor and
Qingqin Qu A Nonconforming Generalized Finite
Element Method for Transmission Problems 555--576
Andrea Bonito and
Irene Kyza and
Ricardo H. Nochetto Time-Discrete Higher-Order ALE
Formulations: Stability . . . . . . . . 577--604
Christian Meyer and
Oliver Thoma A Priori Finite Element Error Analysis
for Optimal Control of the Obstacle
Problem . . . . . . . . . . . . . . . . 605--628
D. P. Hewett and
S. Langdon and
J. M. Melenk A High Frequency $ h p $ Boundary
Element Method for Scattering by Convex
Polygons . . . . . . . . . . . . . . . . 629--653
Paola F. Antonietti and
Lourenco Beiraño da Veiga and
Carlo Lovadina and
Marco Verani Hierarchical a Posteriori Error
Estimators for the Mimetic
Discretization of Elliptic Problems . . 654--675
Bernardo Cockburn and
Wujun Zhang A Posteriori Error Analysis for
Hybridizable Discontinuous Galerkin
Methods for Second Order Elliptic
Problems . . . . . . . . . . . . . . . . 676--693
Dirk Blömker and
Arnulf Jentzen Galerkin Approximations for the
Stochastic Burgers Equation . . . . . . 694--715
Bilal Saad and
Mazen Saad Study of Full Implicit Petroleum
Engineering Finite-Volume Scheme for
Compressible Two-Phase Flow in Porous
Media . . . . . . . . . . . . . . . . . 716--741
Jie Liu Simple and Efficient ALE Methods with
Provable Temporal Accuracy up to Fifth
Order for the Stokes Equations on Time
Varying Domains . . . . . . . . . . . . 743--772
Vít Dolejsí and
Alexandre Ern and
Martin Vohralík A Framework for Robust a Posteriori
Error Control in Unsteady Nonlinear
Advection--Diffusion Problems . . . . . 773--793
L. Beiraño da Veiga and
F. Brezzi and
L. D. Marini Virtual Elements for Linear Elasticity
Problems . . . . . . . . . . . . . . . . 794--812
Li Shan and
Haibiao Zheng Partitioned Time Stepping Method for
Fully Evolutionary Stokes--Darcy Flow
with Beavers--Joseph Interface
Conditions . . . . . . . . . . . . . . . 813--839
Frédérique Charles and
Bruno Després and
Michel Mehrenberger Enhanced Convergence Estimates for
Semi-Lagrangian Schemes Application to
the Vlasov--Poisson Equation . . . . . . 840--863
Youngsoo Ha and
Yeon Ju Lee and
Jungho Yoon Modified Essentially Nonoscillatory
Schemes Based on Exponential Polynomial
Interpolation for Hyperbolic
Conservation Laws . . . . . . . . . . . 864--893
Jeffrey M. Connors and
Jeffrey W. Banks and
Jeffrey A. Hittinger and
Carol S. Woodward A Method to Calculate Numerical Errors
Using Adjoint Error Estimation for
Linear Advection . . . . . . . . . . . . 894--926
Ming-Jun Lai and
Yangyang Xu and
Wotao Yin Improved Iteratively Reweighted Least
Squares for Unconstrained Smoothed $
\ell_q $ Minimization . . . . . . . . . 927--957
Christoph Lehrenfeld and
Arnold Reusken Analysis of a Nitsche XFEM-DG
Discretization for a Class of Two-Phase
Mass Transport Problems . . . . . . . . 958--983
Lars Diening and
Christian Kreuzer and
Endre Süli Finite Element Approximation of Steady
Flows of Incompressible Fluids with
Implicit Power-Law-Like Rheology . . . . 984--1015
Richard S. Falk and
Shawn W. Walker A Mixed Finite Element Method for EWOD
That Directly Computes the Position of
the Moving Interface . . . . . . . . . . 1016--1040
Salim Meddahi and
David Mora and
Rodolfo Rodríguez Finite Element Spectral Analysis for the
Mixed Formulation of the Elasticity
Equations . . . . . . . . . . . . . . . 1041--1063
Giacomo Dimarco and
Lorenzo Pareschi Asymptotic Preserving Implicit-Explicit
Runge--Kutta Methods for Nonlinear
Kinetic Equations . . . . . . . . . . . 1064--1087
Hong Wang and
Danping Yang Wellposedness of Variable-Coefficient
Conservative Fractional Elliptic
Differential Equations . . . . . . . . . 1088--1107
Benjamin Boutin and
Frédéric Coquel and
Philippe G. LeFloch Coupling Techniques for Nonlinear
Hyperbolic Equations. III. The
Well-Balanced Approximation of Thick
Interfaces . . . . . . . . . . . . . . . 1108--1133
Thorsten Rohwedder and
André Uschmajew On Local Convergence of Alternating
Schemes for Optimization of Convex
Problems in the Tensor Train Format . . 1134--1162
Etienne Emmrich and
Aneta Wróblewska-Kami\'nska Convergence of a Full Discretization of
Quasi-linear Parabolic Equations in
Isotropic and Anisotropic Orlicz Spaces 1163--1184
Charles-Edouard Bréhier Analysis of an HMM Time-Discretization
Scheme for a System of Stochastic PDEs 1185--1210
Qiang Du and
Li Tian and
Xuying Zhao A Convergent Adaptive Finite Element
Algorithm for Nonlocal Diffusion and
Peridynamic Models . . . . . . . . . . . 1211--1234
Jing Li and
Xuemin Tu A Nonoverlapping Domain Decomposition
Method for Incompressible Stokes
Equations with Continuous Pressures . . 1235--1253
A. Ibort and
J. M. Pérez-Pardo Numerical Solutions of the Spectral
Problem for Arbitrary Self-Adjoint
Extensions of the One-Dimensional
Schrödinger Equation . . . . . . . . . . 1254--1279
Roberto Barrio and
Hao Jiang and
Sergio Serrano A General Condition Number for
Polynomials . . . . . . . . . . . . . . 1280--1294
Franz Chouly and
Patrick Hild A Nitsche-Based Method for Unilateral
Contact Problems: Numerical Analysis . . 1295--1307
Richard S. Falk and
Michael Neilan Stokes Complexes and the Construction of
Stable Finite Elements with Pointwise
Mass Conservation . . . . . . . . . . . 1308--1326
M. Feischl and
M. Karkulik and
J. M. Melenk and
D. Praetorius Quasi-optimal Convergence Rate for an
Adaptive Boundary Element Method . . . . 1327--1348
Xiaozhe Hu and
Panayot S. Vassilevski and
Jinchao Xu Comparative Convergence Analysis of
Nonlinear AMLI-Cycle Multigrid . . . . . 1349--1369
Manuel J. Castro and
Ulrik S. Fjordholm and
Siddhartha Mishra and
Carlos Parés Entropy Conservative and Entropy Stable
Schemes for Nonconservative Hyperbolic
Systems . . . . . . . . . . . . . . . . 1371--1391
Ramsharan Rangarajan and
Adrian J. Lew Analysis of a Method to Parameterize
Planar Curves Immersed In Triangulations 1392--1420
V. J. Ervin Approximation of Axisymmetric Darcy Flow
Using Mixed Finite Element Methods . . . 1421--1442
Xiaodan Zhao and
Li-Lian Wang and
Ziqing Xie Sharp Error Bounds for Jacobi Expansions
and Gegenbauer--Gauss Quadrature of
Analytic Functions . . . . . . . . . . . 1443--1469
Leszek Plaskota and
Grzegorz W. Wasilkowski and
Yaxi Zhao An Adaptive Algorithm for Weighted
Approximation of Singular Functions over
$ \mathbb {R} $ . . . . . . . . . . . . 1470--1493
Natalia Kopteva and
Torsten Linss Maximum Norm A Posteriori Error
Estimation for Parabolic Problems Using
Elliptic Reconstructions . . . . . . . . 1494--1524
Mitsuhiro T. Nakao and
Takuma Kimura and
Takehiko Kinoshita Constructive A Priori Error Estimates
for a Full Discrete Approximation of the
Heat Equation . . . . . . . . . . . . . 1525--1541
V. Domínguez and
I. G. Graham and
T. Kim Filon--Clenshaw--Curtis Rules for Highly
Oscillatory Integrals with Algebraic
Singularities and Stationary Points . . 1542--1566
Antti Hannukainen Field of Values Analysis of a Two-Level
Preconditioner for the Helmholtz
Equation . . . . . . . . . . . . . . . . 1567--1584
Mark Ainsworth and
Alejandro Allendes and
Gabriel R. Barrenechea and
Richard Rankin On the Adaptive Selection of the
Parameter in Stabilized Finite Element
Approximations . . . . . . . . . . . . . 1585--1609
D. Schötzau and
Ch. Schwab and
T. P. Wihler $ h p $-dGFEM for Second-Order Elliptic
Problems in Polyhedra I: Stability on
Geometric Meshes . . . . . . . . . . . . 1610--1633
Xuefeng Liu and
Shin'ichi Oishi Verified Eigenvalue Evaluation for the
Laplacian over Polygonal Domains of
Arbitrary Shape . . . . . . . . . . . . 1634--1654
Alexandre Ern and
Jean-Luc Guermond Weighting the Edge Stabilization . . . . 1655--1677
Huo-Yuan Duan and
Ping Lin and
Roger C. E. Tan Error Estimates for a Vectorial
Second-Order Elliptic Eigenproblem by
the Local $ L^2 $ Projected $ C^0 $
Finite Element Method . . . . . . . . . 1678--1714
Carsten Carstensen and
Dietmar Gallistl and
Mira Schedensack Quasi-optimal Adaptive Pseudostress
Approximation of the Stokes Equations 1715--1734
Xianjuan Li and
Tao Tang and
Chuanju Xu Parallel in Time Algorithm with
Spectral-Subdomain Enhancement for
Volterra Integral Equations . . . . . . 1735--1756
Victor D. Didenko and
Johan Helsing On the Stability of the Nyström Method
for the Muskhelishvili Equation on
Contours with Corners . . . . . . . . . 1757--1776
Christoph Erath A Posteriori Error Estimates and
Adaptive Mesh Refinement for the
Coupling of the Finite Volume Method and
the Boundary Element Method . . . . . . 1777--1804
J. Brannick and
Y. Chen and
J. Kraus and
L. Zikatanov Algebraic Multilevel Preconditioners for
the Graph Laplacian Based on Matching in
Graphs . . . . . . . . . . . . . . . . . 1805--1827
Lingxue Zhu and
Haijun Wu Preasymptotic Error Analysis of CIP--FEM
and FEM for Helmholtz Equation with High
Wave Number. Part II: $ h p $ Version 1828--1852
Stefan Takacs and
Walter Zulehner Convergence Analysis of All-at-Once
Multigrid Methods for Elliptic Control
Problems under Partial Elliptic
Regularity . . . . . . . . . . . . . . . 1853--1874
M. Herty and
L. Pareschi and
S. Steffensen Implicit-Explicit Runge--Kutta Schemes
for Numerical Discretization of Optimal
Control Problems . . . . . . . . . . . . 1875--1899
Eskil Hansen and
Erik Henningsson A Convergence Analysis of the
Peaceman--Rachford Scheme for Semilinear
Evolution Equations . . . . . . . . . . 1900--1910
Jie Liu Order of Convergence of Splitting
Schemes for Both Deterministic and
Stochastic Nonlinear Schrödinger
Equations . . . . . . . . . . . . . . . 1911--1932
Tan Bui-Thanh and
Leszek Demkowicz and
Omar Ghattas A Unified Discontinuous Petrov--Galerkin
Method and Its Analysis for Friedrichs'
Systems . . . . . . . . . . . . . . . . 1933--1958
Buyang Li and
Weiwei Sun Unconditional Convergence and Optimal
Error Estimates of a Galerkin-Mixed FEM
for Incompressible Miscible Flow in
Porous Media . . . . . . . . . . . . . . 1959--1977
Jianjun Liu and
Liqun Cao and
Ningning Yan Multiscale Asymptotic Analysis and
Computation of Optimal Control for
Elliptic Systems with Constraints . . . 1978--2004
D. Schötzau and
Ch. Schwab and
T. P. Wihler $ h p $-DGFEM for Second Order Elliptic
Problems in Polyhedra II: Exponential
Convergence . . . . . . . . . . . . . . 2005--2035
Rüdiger Frey and
Thorsten Schmidt and
Ling Xu On Galerkin Approximations for the Zakai
Equation with Diffusive and Point
Process Observations . . . . . . . . . . 2036--2062
Marcio Gameiro and
Jean-Philippe Lessard Efficient Rigorous Numerics for
Higher-Dimensional PDEs via
One-Dimensional Estimates . . . . . . . 2063--2087
Iain Smears and
Endre Süli Discontinuous Galerkin Finite Element
Approximation of Nondivergence Form
Elliptic Equations with Cord\`es
Coefficients . . . . . . . . . . . . . . 2088--2106
Hao Ji and
Michael Mascagni and
Yaohang Li Convergence Analysis of Markov Chain
Monte Carlo Linear Solvers Using
Ulam--von Neumann Algorithm . . . . . . 2107--2122
Jérémi Dardé and
Antti Hannukainen and
Nuutti Hyvönen An $ H_\mathsf {div} $-Based Mixed
Quasi-reversibility Method for Solving
Elliptic Cauchy Problems . . . . . . . . 2123--2148
Yiannis Hadjimichael and
Colin B. Macdonald and
David I. Ketcheson and
James H. Verner Strong Stability Preserving Explicit
Runge--Kutta Methods of Maximal
Effective Order . . . . . . . . . . . . 2149--2165
Huangxin Chen and
Peipei Lu and
Xuejun Xu A Hybridizable Discontinuous Galerkin
Method for the Helmholtz Equation with
High Wave Number . . . . . . . . . . . . 2166--2188
Tanja Göckler and
Volker Grimm Convergence Analysis of an Extended
Krylov Subspace Method for the
Approximation of Operator Functions in
Exponential Integrators . . . . . . . . 2189--2213
K. Liu and
T. A. Manteuffel and
S. F. McCormick and
J. W. Ruge and
L. Tang Hybrid First-Order System Least Squares
Finite Element Methods with Application
to Stokes Equations . . . . . . . . . . 2214--2237
Hui Liang and
Hermann Brunner Integral-Algebraic Equations: Theory of
Collocation Methods I . . . . . . . . . 2238--2259
Z. W. Yang and
H. Brunner Blow-Up Behavior of Collocation
Solutions to Hammerstein-Type Volterra
Integral Equations . . . . . . . . . . . 2260--2282
K. Kumar and
I. S. Pop and
F. A. Radu Convergence Analysis of Mixed Numerical
Schemes for Reactive Flow in a Porous
Medium . . . . . . . . . . . . . . . . . 2283--2308
Omar Lakkis and
Anotida Madzvamuse and
Chandrasekhar Venkataraman Implicit--Explicit Timestepping with
Finite Element Approximation of
Reaction--Diffusion Systems on Evolving
Domains . . . . . . . . . . . . . . . . 2309--2330
Zhiming Chen and
Xueshuang Xiang A Source Transfer Domain Decomposition
Method for Helmholtz Equations in
Unbounded Domain . . . . . . . . . . . . 2331--2356
Assyr Abdulle and
Ping Lin and
Alexander V. Shapeev A Priori and A Posteriori $ W^{1, \infty
} $ Error Analysis of a QC Method for
Complex Lattices . . . . . . . . . . . . 2357--2379
Ana Alonso Rodríguez and
Enrico Bertolazzi and
Riccardo Ghiloni and
Alberto Valli Construction of a Finite Element Basis
of the First de Rham Cohomology Group
and Numerical Solution of $3$D
Magnetostatic Problems . . . . . . . . . 2380--2402
Patricio Farrell and
Holger Wendland RBF Multiscale Collocation for Second
Order Elliptic Boundary Value Problems 2403--2425
Claude Jeffrey Gittelson Convergence Rates of Multilevel and
Sparse Tensor Approximations for a
Random Elliptic PDE . . . . . . . . . . 2426--2447
Takahito Kashiwabara Finite Element Method for Stokes
Equations under Leak Boundary Condition
of Friction Type . . . . . . . . . . . . 2448--2469
Sean O. Settle and
Craig C. Douglas and
Imbunm Kim and
Dongwoo Sheen On the Derivation of Highest-Order
Compact Finite Difference Schemes for
the One- and Two-Dimensional Poisson
Equation with Dirichlet Boundary
Conditions . . . . . . . . . . . . . . . 2470--2490
Markus Bachmayr Integration of Products of Gaussians and
Wavelets with Applications to Electronic
Structure Calculations . . . . . . . . . 2491--2513
Leszek Demkowicz and
Norbert Heuer Robust DPG Method for
Convection-Dominated Diffusion Problems 2514--2537
E. Fuselier and
T. Hangelbroek and
F. J. Narcowich and
J. D. Ward and
G. B. Wright Localized Bases for Kernel Spaces on the
Unit Sphere . . . . . . . . . . . . . . 2538--2562
Wenbin Chen and
Max Gunzburger and
Dong Sun and
Xiaoming Wang Efficient and Long-Time Accurate
Second-Order Methods for the
Stokes--Darcy System . . . . . . . . . . 2563--2584
Yves Achdou and
Fabio Camilli and
Italo Capuzzo-Dolcetta Mean Field Games: Convergence of a
Finite Difference Method . . . . . . . . 2585--2612
F. Ar\`andiga On the Order of Nonuniform Monotone
Cubic Hermite Interpolants . . . . . . . 2613--2633
C. D'Apice and
R. Manzo and
B. Piccoli Numerical Schemes for the Optimal Input
Flow of a Supply Chain . . . . . . . . . 2634--2650
Jun Hu and
Zhongci Shi A Lower Bound of the $ L^2 $ Norm Error
Estimate for the Adini Element of the
Biharmonic Equation . . . . . . . . . . 2651--2659
Charles L. Epstein and
Leslie Greengard and
Andreas Klöckner On the Convergence of Local Expansions
of Layer Potentials . . . . . . . . . . 2660--2679
Xuping Zhang and
Jintao Zhang and
Bo Yu Eigenfunction Expansion Method for
Multiple Solutions of Semilinear
Elliptic Equations with Polynomial
Nonlinearity . . . . . . . . . . . . . . 2680--2699
Peng Chen and
Alfio Quarteroni and
Gianluigi Rozza Stochastic Optimal Robin Boundary
Control Problems of Advection-Dominated
Elliptic Equations . . . . . . . . . . . 2700--2722
Arnold Reusken A Finite Element Level Set Redistancing
Method Based on Gradient Recovery . . . 2723--2745
Jiang Zhu and
Jiansong Zhang and
Abimael F. D. Loula and
Luiz Bevilacqua Mixed Variational Formulation and
Numerical Analysis of Thermally Coupled
Nonlinear Darcy Flows . . . . . . . . . 2746--2772
Lutz Kämmerer Reconstructing Hyperbolic Cross
Trigonometric Polynomials by Sampling
along Rank-$1$ Lattices . . . . . . . . 2773--2796
Dmitriy Leykekhman and
Boris Vexler Optimal A Priori Error Estimates of
Parabolic Optimal Control Problems with
Pointwise Control . . . . . . . . . . . 2797--2821
Qinghai Zhang On a Family of Unsplit Advection
Algorithms for Volume-of-Fluid Methods 2822--2850
A. Baskaran and
J. S. Lowengrub and
C. Wang and
S. M. Wise Convergence Analysis of a Second Order
Convex Splitting Scheme for the Modified
Phase Field Crystal Equation . . . . . . 2851--2873
Aziz Takhirov Stokes--Brinkman Lagrange
Multiplier/Fictitious Domain Method for
Flows in Pebble Bed Geometries . . . . . 2874--2886
David I. Ketcheson and
Colin B. MacDonald and
Steven J. Ruuth Spatially Partitioned Embedded
Runge--Kutta Methods . . . . . . . . . . 2887--2910
Andrea Cangiani and
Emmanuil H. Georgoulis and
Max Jensen Discontinuous Galerkin Methods for Mass
Transfer through Semipermeable Membranes 2911--2934
Carsten Carstensen and
Dietmar Gallistl and
Mira Schedensack Discrete Reliability for
Crouzeix--Raviart FEMs . . . . . . . . . 2935--2955
Sarah Day and
William D. Kalies Rigorous Computation of the Global
Dynamics of Integrodifference Equations
with Smooth Nonlinearities . . . . . . . 2957--2983
A. Kuznetsov On the Convergence of the
Gaver--Stehfest Algorithm . . . . . . . 2984--2998
E. Carlini and
M. Falcone and
Ph. Hoch A Generalized Fast Marching Method on
Unstructured Triangular Meshes . . . . . 2999--3035
G. Grün On Convergent Schemes for Diffuse
Interface Models for Two-Phase Flow of
Incompressible Fluids with General Mass
Densities . . . . . . . . . . . . . . . 3036--3061
Sébastien Loisel Condition Number Estimates for the
Nonoverlapping Optimized Schwarz Method
and the $2$-Lagrange Multiplier Method
for General Domains and Cross Points . . 3062--3083
Raymond L. Speth and
William H. Green and
Shev MacNamara and
Gilbert Strang Balanced Splitting and Rebalanced
Splitting . . . . . . . . . . . . . . . 3084--3105
Andrea Bonito and
Ronald A. DeVore and
Ricardo H. Nochetto Adaptive Finite Element Methods for
Elliptic Problems with Discontinuous
Coefficients . . . . . . . . . . . . . . 3106--3134
M. V. Tretyakov and
Z. Zhang A Fundamental Mean-Square Convergence
Theorem for SDEs with Locally Lipschitz
Coefficients and Its Applications . . . 3135--3162
Peng Chen and
Alfio Quarteroni and
Gianluigi Rozza A Weighted Reduced Basis Method for
Elliptic Partial Differential Equations
with Random Input Data . . . . . . . . . 3163--3185
Xue Luo and
Stephen S.-T. Yau Hermite Spectral Method with Hyperbolic
Cross Approximations to High-Dimensional
Parabolic PDEs . . . . . . . . . . . . . 3186--3212
Åke Brännström and
Linus Carlsson and
Daniel Simpson On the Convergence of the Escalator
Boxcar Train . . . . . . . . . . . . . . 3213--3231
Rémi Carles On Fourier Time-Splitting Methods for
Nonlinear Schrödinger Equations in the
Semiclassical Limit . . . . . . . . . . 3232--3258
Christian Waluga and
Barbara Wohlmuth Quasi-optimal A Priori Interface Error
Bounds and A Posteriori Estimates for
the Interior Penalty Method . . . . . . 3259--3279
Jisheng Kou and
Shuyu Sun Convergence of Discontinuous Galerkin
Methods for Incompressible Two-Phase
Flow in Heterogeneous Media . . . . . . 3280--3306
Bernhard Beckermann and
Daniel Kressner and
Christine Tobler An Error Analysis of Galerkin Projection
Methods for Linear Systems with Tensor
Product Structure . . . . . . . . . . . 3307--3326
Hyea Hyun Kim and
Eric T. Chung and
Chak Shing Lee A Staggered Discontinuous Galerkin
Method for the Stokes System . . . . . . 3327--3350
Daniel Elfverson and
Emmanuil H. Georgoulis and
Axel Målqvist and
Daniel Peterseim Convergence of a Discontinuous Galerkin
Multiscale Method . . . . . . . . . . . 3351--3372
Benjamin Martin and
Alexandre Goldsztejn and
Laurent Granvilliers and
Christophe Jermann Certified Parallelotope Continuation for
One-Manifolds . . . . . . . . . . . . . 3373--3401
Giacomo Gigante and
Matteo Pozzoli and
Christian Vergara Optimized Schwarz Methods for the
Diffusion-Reaction Problem with
Cylindrical Interfaces . . . . . . . . . 3402--3430
Vu Thai Luan and
Alexander Ostermann Exponential $B$-Series: The Stiff Case 3431--3445
Deren Han and
Xiaoming Yuan Local Linear Convergence of the
Alternating Direction Method of
Multipliers for Quadratic Programs . . . 3446--3457
Xiaochuan Tian and
Qiand Du Analysis and Comparison of Different
Approximations to Nonlocal Diffusion and
Linear Peridynamic Equations . . . . . . 3458--3482
José C. M. Duque and
Rui M. P. Almeida and
Stanislav N. Antontsev Convergence of the Finite Element Method
for the Porous Media Equation with
Variable Exponent . . . . . . . . . . . 3483--3504
Rodolfo Araya and
Christopher Harder and
Diego Paredes and
Frédéric Valentin Multiscale Hybrid-Mixed Method . . . . . 3505--3531
Thao-Phuong Hoang and
Jérôme Jaffré and
Caroline Japhet and
Michel Kern and
Jean E. Roberts Space--time Domain Decomposition Methods
for Diffusion Problems in Mixed
Formulations . . . . . . . . . . . . . . 3532--3559
Jean-Philippe Lessard and
Christian Reinhardt Rigorous Numerics for Nonlinear
Differential Equations Using Chebyshev
Series . . . . . . . . . . . . . . . . . 1--22
Songting Luo and
Jianliang Qian and
Robert Burridge High-Order Factorization Based
High-Order Hybrid Fast Sweeping Methods
for Point-Source Eikonal Equations . . . 23--44
E. Carlini and
F. J. Silva A Fully Discrete Semi-Lagrangian Scheme
for a First Order Mean Field Game
Problem . . . . . . . . . . . . . . . . 45--67
Hongjiong Tian and
Quanhong Yu and
Jiaoxun Kuang Asymptotic Stability of Linear Neutral
Delay Differential-Algebraic Equations
and Runge--Kutta Methods . . . . . . . . 68--82
Fabian Brunner and
Florin A. Radu and
Peter Knabner Analysis of an Upwind-Mixed Hybrid
Finite Element Method for Transport
Problems . . . . . . . . . . . . . . . . 83--102
J. Willems Robust Multilevel Methods for General
Symmetric Positive Definite Operators 103--124
Ben Adcock and
Anders C. Hansen and
Alexei Shadrin A Stability Barrier for Reconstructions
from Fourier Samples . . . . . . . . . . 125--139
Lukas Einkemmer and
Alexander Ostermann Convergence Analysis of Strang Splitting
for Vlasov-Type Equations . . . . . . . 140--155
Qiqi Wang Convergence of the Least Squares
Shadowing Method for Computing
Derivative of Ergodic Averages . . . . . 156--170
H. Egger and
U. Rüde and
B. Wohlmuth Energy-Corrected Finite Element Methods
for Corner Singularities . . . . . . . . 171--193
Milan Hladík New Operator and Method for Solving Real
Preconditioned Interval Linear Equations 194--206
Yue Wang and
Jiequan Li Numerical Defects of the HLL Scheme and
Dissipation Matrices for the Euler
Equations . . . . . . . . . . . . . . . 207--219
Matthew F. Causley and
Andrew J. Christlieb Higher Order $A$-Stable Schemes for the
Wave Equation Using a Successive
Convolution Approach . . . . . . . . . . 220--235
Adriano Festa and
Maurizio Falcone An Approximation Scheme for an Eikonal
Equation with Discontinuous Coefficient 236--257
Panayot S. Vassilevski and
Umberto Villa A Mixed Formulation for the Brinkman
Problem . . . . . . . . . . . . . . . . 258--281
Shuo Zhang and
Jinchao Xu Optimal Solvers for Fourth-Order PDEs
Discretized on Unstructured Grids . . . 282--307
Ivana Sebestová and
Tomás Vejchodský Two-Sided Bounds for Eigenvalues of
Differential Operators with Applications
to Friedrichs, Poincaré, Trace, and
Similar Constants . . . . . . . . . . . 308--329
Noel J. Walkington A $ C^1 $ Tetrahedral Finite Element
without Edge Degrees of Freedom . . . . 330--342
Roland Griesmaier and
Martin Hanke and
John Sylvester Far Field Splitting for the Helmholtz
Equation . . . . . . . . . . . . . . . . 343--362
Sören Bartels and
Ricardo H. Nochetto and
Abner J. Salgado Discrete Total Variation Flows without
Regularization . . . . . . . . . . . . . 363--385
P. F. Antonietti and
L. Beiraño da Veiga and
D. Mora and
M. Verani A Stream Virtual Element Formulation of
the Stokes Problem on Polygonal Meshes 386--404
Qinwu Xu and
Jan S. Hesthaven Discontinuous Galerkin Method for
Fractional Convection--Diffusion
Equations . . . . . . . . . . . . . . . 405--423
Robert I. A. Patterson and
Wolfgang Wagner Cell Size Error in Stochastic Particle
Methods for Coagulation Equations with
Advection . . . . . . . . . . . . . . . 424--442
Miodrag M. Spalevi\'c Error Bounds and Estimates for
Gauss--Turán Quadrature Formulae of
Analytic Functions . . . . . . . . . . . 443--467
Mihai Anitescu and
Xiaoyan Zeng and
Emil M. Constantinescu A Low-Memory Approach for Best-State
Estimation of Hidden Markov Models with
Model Error . . . . . . . . . . . . . . 468--495
Yang Liu and
Yoichiro Mori $ L^p $ Convergence of the Immersed
Boundary Method for Stationary Stokes
Problems . . . . . . . . . . . . . . . . 496--514
Michael Floater and
Andrew Gillette and
N. Sukumar Gradient Bounds for Wachspress
Coordinates on Polytopes . . . . . . . . 515--532
Maxime Gazeau Probability and Pathwise Order of
Convergence of a Semidiscrete Scheme for
the Stochastic Manakov Equation . . . . 533--553
Ch. Chalons and
P. Engel and
Ch. Rohde A Conservative and Convergent Scheme for
Undercompressive Shock Waves . . . . . . 554--579
Peter Benner and
Tatjana Stykel Numerical Solution of Projected
Algebraic Riccati Equations . . . . . . 581--600
M. Feischl and
T. Führer and
D. Praetorius Adaptive FEM with Optimal Convergence
Rates for a Certain Class of
Nonsymmetric and Possibly Nonlinear
Problems . . . . . . . . . . . . . . . . 601--625
Laurent Gosse A Two-Dimensional Version of the Godunov
Scheme for Scalar Balance Laws . . . . . 626--652
Burak Aksoylu and
Zuhal Unlu Conditioning Analysis of Nonlocal
Integral Operators in Fractional Sobolev
Spaces . . . . . . . . . . . . . . . . . 653--677
Keith J. Galvin and
Leo G. Rebholz and
Catalin Trenchea Efficient, Unconditionally Stable, and
Optimally Accurate FE Algorithms for
Approximate Deconvolution Models . . . . 678--707
Sören Bartels Quasi-optimal Error Estimates for
Implicit Discretizations of
Rate-Independent Evolutions . . . . . . 708--716
Oliver Ebner Stochastic Aspects of Nonlinear
Refinement Schemes . . . . . . . . . . . 717--734
F. M. G. Magpantay and
N. Kosovali\'c and
J. Wu An Age-Structured Population Model with
State-Dependent Delay: Derivation and
Numerical Integration . . . . . . . . . 735--756
Lukas Einkemmer and
Alexander Ostermann Convergence Analysis of a Discontinuous
Galerkin/Strang Splitting Approximation
for the Vlasov--Poisson Equations . . . 757--778
Patrick Ciarlet, Jr. and
Haijun Wu and
Jun Zou Edge Element Methods for Maxwell's
Equations with Strong Convergence for
Gauss' Laws . . . . . . . . . . . . . . 779--807
Xu Yang and
Jiwei Zhang Computation of the Schrödinger Equation
in the Semiclassical Regime on an
Unbounded Domain . . . . . . . . . . . . 808--831
Miroslav S. Prani\'c and
Lothar Reichel Rational Gauss Quadrature . . . . . . . 832--851
John R. Singler New POD Error Expressions, Error Bounds,
and Asymptotic Results for Reduced Order
Models of Parabolic PDEs . . . . . . . . 852--876
Kai Diethelm Error Bounds for the Numerical
Integration of Functions with Limited
Smoothness . . . . . . . . . . . . . . . 877--879
Fleurianne Bertrand and
Steffen Münzenmaier and
Gerhard Starke First-Order System Least Squares on
Curved Boundaries: Lowest-Order
Raviart--Thomas Elements . . . . . . . . 880--894
Janosch Rieger Semi-Implicit Euler Schemes for Ordinary
Differential Inclusions . . . . . . . . 895--914
Eric Chung and
Bernardo Cockburn and
Guosheng Fu The Staggered DG Method is the Limit of
a Hybridizable DG Method . . . . . . . . 915--932
Buyang Li and
Huadong Gao and
Weiwei Sun Unconditionally Optimal Error Estimates
of a Crank--Nicolson Galerkin Method for
the Nonlinear Thermistor Equations . . . 933--954
Hideki Murakawa Error Estimates for Discrete-Time
Approximations of Nonlinear
Cross-Diffusion Systems . . . . . . . . 955--974
Yoshitaka Watanabe and
Kaori Nagatou and
Michael Plum and
Mitsuhiro T. Nakao Verified Computations of Eigenvalue
Exclosures for Eigenvalue Problems in
Hilbert Spaces . . . . . . . . . . . . . 975--992
Iain Smears and
Endre Süli Discontinuous Galerkin Finite Element
Approximation of
Hamilton--Jacobi--Bellman Equations with
Cordes Coefficients . . . . . . . . . . 993--1016
Yingda Cheng and
Irene M. Gamba and
Fengyan Li and
Philip J. Morrison Discontinuous Galerkin Methods for the
Vlasov--Maxwell Equations . . . . . . . 1017--1049
Dimitris Vartziotis and
Benjamin Himpel Efficient Mesh Optimization Using the
Gradient Flow of the Mean Volume . . . . 1050--1075
Mohammad D. Al-Khaleel and
Martin J. Gander and
Albert E. Ruehli Optimization of Transmission Conditions
in Waveform Relaxation Techniques for RC
Circuits . . . . . . . . . . . . . . . . 1076--1101
Weizhu Bao and
Yongyong Cai Uniform and Optimal Error Estimates of
an Exponential Wave Integrator Sine
Pseudospectral Method for the Nonlinear
Schrödinger Equation with Wave Operator 1103--1127
Jan Baldeaux and
Michael Gnewuch Optimal Randomized Multilevel Algorithms
for Infinite-Dimensional Integration on
Function Spaces with ANOVA-Type
Decomposition . . . . . . . . . . . . . 1128--1155
Giorgos Arampatzis and
Markos A. Katsoulakis and
Petr Plechác Parallelization, Processor Communication
and Error Analysis in Lattice Kinetic
Monte Carlo . . . . . . . . . . . . . . 1156--1182
Huadong Gao and
Buyang Li and
Weiwei Sun Optimal Error Estimates of Linearized
Crank--Nicolson Galerkin FEMs for the
Time-Dependent Ginzburg--Landau
Equations in Superconductivity . . . . . 1183--1202
Thorsten Hohage and
Frank Werner Convergence Rates for Inverse Problems
with Impulsive Noise . . . . . . . . . . 1203--1221
Anne Gelb and
Guohui Song A Frame Theoretic Approach to the
Nonuniform Fast Fourier Transform . . . 1222--1242
Ralf Kornhuber and
Christoph Schwab and
Maren-Wanda Wolf Multilevel Monte Carlo Finite Element
Methods for Stochastic Elliptic
Variational Inequalities . . . . . . . . 1243--1268
Laurence Halpern and
Florence Hubert A Finite Volume Ventcell--Schwarz
Algorithm for Advection--Diffusion
Equations . . . . . . . . . . . . . . . 1269--1291
Hong Wang and
Danping Yang and
Shengfeng Zhu Inhomogeneous Dirichlet Boundary-Value
Problems of Space-Fractional Diffusion
Equations and their Finite Element
Approximations . . . . . . . . . . . . . 1292--1310
Stéphane Descombes and
Max Duarte and
Thierry Dumont and
Frédérique Laurent and
Violaine Louvet and
Marc Massot Analysis of Operator Splitting in the
Nonasymptotic Regime for Nonlinear
Reaction--Diffusion Equations.
Application to the Dynamics of Premixed
Flames . . . . . . . . . . . . . . . . . 1311--1334
Carsten Carstensen and
Leszek Demkowicz and
Jay Gopalakrishnan A Posteriori Error Control for DPG
Methods . . . . . . . . . . . . . . . . 1335--1353
Maxim A. Olshanskii and
Arnold Reusken and
Xianmin Xu An Eulerian Space--time Finite Element
Method for Diffusion Problems on
Evolving Surfaces . . . . . . . . . . . 1354--1377
Robert I. McLachlan and
Ari Stern Modified Trigonometric Integrators . . . 1378--1397
Noel J. Walkington Combined DG--CG Time Stepping for Wave
Equations . . . . . . . . . . . . . . . 1398--1417
Minghua Chen and
Weihua Deng Fourth Order Accurate Scheme for the
Space Fractional Diffusion Equations . . 1418--1438
Fábio Margotti and
Andreas Rieder and
Antonio Leitaño A Kaczmarz Version of the
REGINN--Landweber Iteration for
Ill-Posed Problems in Banach Spaces . . 1439--1465
Barbora Benesová and
Christof Melcher and
Endre Süli An Implicit Midpoint Spectral
Approximation of Nonlocal Cahn--Hilliard
Equations . . . . . . . . . . . . . . . 1466--1496
Caroline Japhet and
Yvon Maday and
Frédéric Nataf Robin Schwarz Algorithm for the NICEM
Method: The $ \mathbf {P}_q $ Finite
Element Case . . . . . . . . . . . . . . 1497--1524
Patrick Henning and
Axel Målqvist and
Daniel Peterseim Two-Level Discretization Techniques for
Ground State Computations of
Bose--Einstein Condensates . . . . . . . 1525--1550
Laurent Sorber and
Marc Van Barel and
Lieven De Lathauwer Numerical Solution of Bivariate and
Polyanalytic Polynomial Systems . . . . 1551--1572
Jean-Marie Mirebeau Anisotropic Fast-Marching on Cartesian
Grids Using Lattice Basis Reduction . . 1573--1599
Assyr Abdulle and
Gilles Vilmart and
Konstantinos C. Zygalakis High Order Numerical Approximation of
the Invariant Measure of Ergodic SDEs 1600--1622
Nan Li and
Lihong Zhi Verified Error Bounds for Isolated
Singular Solutions of Polynomial Systems 1623--1640
Xiaochuan Tian and
Qiang Du Asymptotically Compatible Schemes and
Applications to Robust Discretization of
Nonlocal Models . . . . . . . . . . . . 1641--1665
M. Bessemoulin-Chatard and
C. Chainais-Hillairet and
M.-H. Vignal Study of a Finite Volume Scheme for the
Drift-Diffusion System. Asymptotic
Behavior in the Quasi-Neutral Limit . . 1666--1691
Lennard Kamenski and
Weizhang Huang How a Nonconvergent Recovered Hessian
Works in Mesh Adaptation . . . . . . . . 1692--1708
C. Carstensen and
C. Merdon Refined Fully Explicit a Posteriori
Residual-Based Error Control . . . . . . 1709--1728
Santiago Badia and
Ramon Codina and
Hector Espinoza Stability, Convergence, and Accuracy of
Stabilized Finite Element Methods for
the Wave Equation in Mixed Form . . . . 1729--1752
T. Köppl and
B. Wohlmuth Optimal A Priori Error Estimates for an
Elliptic Problem with Dirac Right-Hand
Side . . . . . . . . . . . . . . . . . . 1753--1769
Massimo Fornasier and
Valeriya Naumova and
Sergei V. Pereverzyev Parameter Choice Strategies for
Multipenalty Regularization . . . . . . 1770--1794
Anthony P. Austin and
Peter Kravanja and
Lloyd N. Trefethen Numerical Algorithms Based on Analytic
Function Values at Roots of Unity . . . 1795--1821
Guido Kanschat and
Natasha Sharma Divergence-Conforming Discontinuous
Galerkin Methods and $ C^0 $ Interior
Penalty Methods . . . . . . . . . . . . 1822--1842
S. Maset and
M. Zennaro Good Behavior with Respect to the
Stiffness in the Numerical Integration
of Retarded Functional Differential
Equations . . . . . . . . . . . . . . . 1843--1866
Iván Area and
Dimitar K. Dimitrov and
Eduardo Godoy and
Vanessa Paschoa Approximate Calculation of Sums I:
Bounds for the Zeros of Gram Polynomials 1867--1886
Ben Adcock and
Mark Richardson New Exponential Variable Transform
Methods for Functions with Endpoint
Singularities . . . . . . . . . . . . . 1887--1912
Tobin A. Driscoll and
J. A. C. Weideman Optimal Domain Splitting for
Interpolation by Chebyshev Polynomials 1913--1927
Liqian Peng and
Kamran Mohseni An Online Manifold Learning Approach for
Model Reduction of Dynamical Systems . . 1928--1952
Chang-Tao Sheng and
Zhong-Qing Wang and
Ben-Yu Guo A Multistep Legendre--Gauss Spectral
Collocation Method for Nonlinear
Volterra Integral Equations . . . . . . 1953--1980
Martin J. Gander and
Yingxiang Xu Optimized Schwarz Methods for Circular
Domain Decompositions with Overlap . . . 1981--2004
Jianfeng Lu and
Pingbing Ming Stability Of A Force-Based Hybrid Method
With Planar Sharp Interface . . . . . . 2005--2026
J. Zhou and
X. Hu and
L. Zhong and
S. Shu and
L. Chen Two-Grid Methods for Maxwell Eigenvalue
Problems . . . . . . . . . . . . . . . . 2027--2047
Juhi Jang and
Fengyan Li and
Jing-Mei Qiu and
Tao Xiong Analysis of Asymptotic Preserving
DG--IMEX Schemes for Linear Kinetic
Transport Equations in a Diffusive
Scaling . . . . . . . . . . . . . . . . 2048--2072
Trygve K. Karper and
Franziska Weber A New Angular Momentum Method for
Computing Wave Maps into Spheres . . . . 2073--2091
Maxim A. Olshanskii and
Arnold Reusken Error Analysis of a Space--time Finite
Element Method for Solving PDEs on
Evolving Surfaces . . . . . . . . . . . 2092--2120
D. Braess and
T. Fraunholz and
R. H. W. Hoppe An Equilibrated A Posteriori Error
Estimator for the Interior Penalty
Discontinuous Galerkin Method . . . . . 2121--2136
Klaus Deckelnick and
Charles M. Elliott and
Thomas Ranner Unfitted Finite Element Methods Using
Bulk Meshes for Surface Partial
Differential Equations . . . . . . . . . 2137--2162
Jean-Luc Guermond and
Murtazo Nazarov and
Bojan Popov and
Yong Yang A Second-Order Maximum Principle
Preserving Lagrange Finite Element
Technique for Nonlinear Scalar
Conservation Equations . . . . . . . . . 2163--2182
Derek Olson and
Pavel B. Bochev and
Mitchell Luskin and
Alexander V. Shapeev An Optimization-based
Atomistic-to-Continuum Coupling Method 2183--2204
Congpei An and
Xiaojun Chen and
Ian H. Sloan and
Robert S. Womersley Corrigendum: Regularized Least Squares
Approximations on the Sphere Using
Spherical Designs . . . . . . . . . . . 2205--2206
Faker Ben Belgacem and
Christine Bernardi and
Frédéric Hecht and
Stéphanie Salmon Stabilized Finite Elements for a
Reaction-Dispersion Saddle-Point Problem
with NonConstant Coefficients . . . . . 2207--2226
David I. Ketcheson and
Lajos Lóczi and
Matteo Parsani Internal Error Propagation in Explicit
Runge--Kutta Methods . . . . . . . . . . 2227--2249
Silke Glas and
Karsten Urban On Noncoercive Variational Inequalities 2250--2271
Bangti Jin and
Raytcho Lazarov and
Joseph Pasciak and
Zhi Zhou Error Analysis of a Finite Element
Method for the Space-Fractional
Parabolic Equation . . . . . . . . . . . 2272--2294
Ralf Hiptmair and
Carlos Jerez-Hanckes and
Carolina Urzúa-Torres Mesh-Independent Operator
Preconditioning for Boundary Elements on
Open Curves . . . . . . . . . . . . . . 2295--2314
Stefan Frei and
Thomas Richter A Locally Modified Parametric Finite
Element Method for Interface Problems 2315--2334
Oliver Kolb On the Full and Global Accuracy of a
Compact Third Order WENO Scheme . . . . 2335--2355
Xiaobing Feng and
Haijun Wu An Absolutely Stable Discontinuous
Galerkin Method for the Indefinite
Time-Harmonic Maxwell Equations with
Large Wave Number . . . . . . . . . . . 2356--2380
Yongxiang Liu and
Xuejun Xu A Robin-type Domain Decomposition Method
with Red--Black Partition . . . . . . . 2381--2399
A. Kimeswenger and
O. Steinbach and
G. Unger Coupled Finite And Boundary Element
Methods for Fluid-Solid Interaction
Eigenvalue Problems . . . . . . . . . . 2400--2414
J. Deteix and
A. Jendoubi and
D. Yakoubi A Coupled Prediction Scheme for Solving
the Navier--Stokes and
Convection--Diffusion Equations . . . . 2415--2439
John C. Butcher and
Yousaf Habib and
Adrian T. Hill and
Terence J. T. Norton The Control of Parasitism in
$G$-symplectic Methods . . . . . . . . . 2440--2465
Quentin Mérigot and
Édouard Oudet Handling Convexity-Like Constraints in
Variational Problems . . . . . . . . . . 2466--2487
Weizhu Bao and
Yongyong Cai and
Xiaofei Zhao A Uniformly Accurate Multiscale Time
Integrator Pseudospectral Method for the
Klein--Gordon Equation in the
Nonrelativistic Limit Regime . . . . . . 2488--2511
K. Mustapha and
B. Abdallah and
K. M. Furati A Discontinuous Petrov--Galerkin Method
for Time-Fractional Diffusion Equations 2512--2529
Ying Jiang and
Bo Wang and
Yuesheng Xu A Fast Fourier--Galerkin Method Solving
a Boundary Integral Equation for the
Biharmonic Equation . . . . . . . . . . 2530--2554
Waixiang Cao and
Zhimin Zhang and
Qingsong Zou Superconvergence of Discontinuous
Galerkin Methods for Linear Hyperbolic
Equations . . . . . . . . . . . . . . . 2555--2573
Huadong Gao Optimal Error Estimates of a Linearized
Backward Euler FEM for the
Landau--Lifshitz Equation . . . . . . . 2574--2593
Mihály Kovács and
Stig Larsson and
Ali Mesforush Erratum: Finite Element Approximation of
the Cahn--Hilliard--Cook Equation . . . 2594--2597
Fanhai Zeng and
Fawang Liu and
Changpin Li and
Kevin Burrage and
Ian Turner and
V. Anh A Crank--Nicolson ADI Spectral Method
for a Two-Dimensional Riesz Space
Fractional Nonlinear Reaction--Diffusion
Equation . . . . . . . . . . . . . . . . 2599--2622
Buyang Li and
Weiwei Sun Linearized FE Approximations to a
Nonlinear Gradient Flow . . . . . . . . 2623--2646
Huiyuan Li and
Yuan Xu Spectral Approximation on the Unit Ball 2647--2675
Josef Dick and
Frances Y. Kuo and
Quoc T. Le Gia and
Dirk Nuyens and
Christoph Schwab Higher Order QMC Petrov--Galerkin
Discretization for Affine Parametric
Operator Equations with Random Field
Inputs . . . . . . . . . . . . . . . . . 2676--2702
Norbert Heuer and
Felipe Pinochet Ultra-weak Formulation of a
Hypersingular Integral Equation on
Polygons and DPG Method with Optimal
Test Functions . . . . . . . . . . . . . 2703--2721
Frank Filbir and
Stefan Kunis and
Ruben Seyfried Effective Discretization of Direct
Reconstruction Schemes For Photoacoustic
Imaging In Spherical Geometries . . . . 2722--2742
Douglas N. Arnold and
Jeonghun J. Lee Mixed Methods for Elastodynamics with
Weak Symmetry . . . . . . . . . . . . . 2743--2769
Pascal Noble and
Jean-Paul Vila Stability Theory for Difference
Approximations of Euler--Korteweg
Equations and Application to Thin Film
Flows . . . . . . . . . . . . . . . . . 2770--2791
L. Monasse and
R. Monneau Gradient Entropy Estimate and
Convergence of a Semi-Explicit Scheme
for Diagonal Hyperbolic Systems . . . . 2792--2814
Jean-François Chassagneux Linear Multistep Schemes for BSDEs . . . 2815--2836
Konstantinos Chrysafinos and
Efthimios N. Karatzas Error Estimates for Discontinuous
Galerkin Time-Stepping Schemes for Robin
Boundary Control Problems Constrained to
Parabolic PDEs . . . . . . . . . . . . . 2837--2862
M. Fasondini and
S. W. Schoombie Spurious Resonance in SemiDiscrete
Methods for the Korteweg--de Vries
Equation . . . . . . . . . . . . . . . . 2863--2882
Kenneth Duru and
Gunilla Kreiss Boundary Waves and Stability of the
Perfectly Matched Layer for the Two
Space Dimensional Elastic Wave Equation
in Second Order Form . . . . . . . . . . 2883--2904
Chunxiong Zhen Optimal Error Estimates for First-Order
Gaussian Beam Approximations to the
Schrödinger Equation . . . . . . . . . . 2905--2930
B. Gmeiner and
C. Waluga and
B. Wohlmuth Local Mass-Corrections for Continuous
Pressure Approximations of
Incompressible Flow . . . . . . . . . . 2931--2956
Owe Axelsson and
János Karátson and
Balázs Kovács Robust Preconditioning Estimates for
Convection-Dominated Elliptic Problems
via a Streamline Poincaré--Friedrichs
Inequality . . . . . . . . . . . . . . . 2957--2976
Clara Mertens and
Raf Vandebril Multiple Recurrences and the Associated
Matrix Structures Stemming From Normal
Matrices . . . . . . . . . . . . . . . . 2977--2999
Jilu Wang and
Zhiyong Si and
Weiwei Sun A New Error Analysis of
Characteristics-Mixed FEMs for Miscible
Displacement in Porous Media . . . . . . 3000--3020
Jirí Hrivnák and
Lenka Motlochová Discrete Transforms and Orthogonal
Polynomials of (Anti)Symmetric
Multivariate Cosine Functions . . . . . 3021--3055
Yanghong Huang and
Adam Oberman Numerical Methods for the Fractional
Laplacian: a Finite
Difference-Quadrature Approach . . . . . 3056--3084
Jehanzeb Hameed Chaudhry and
Eric C. Cyr and
Kuo Liu and
Thomas A. Manteuffel and
Luke N. Olson and
Lei Tang Enhancing Least-Squares Finite Element
Methods Through a Quantity-of-Interest 3085--3105
David F. Anderson and
Desmond J. Higham and
Yu Sun Complexity of Multilevel Monte Carlo
Tau-Leaping . . . . . . . . . . . . . . 3106--3127
Eskil Hansen and
Tony Stillfjord Convergence Analysis for Splitting of
the Abstract Differential Riccati
Equation . . . . . . . . . . . . . . . . 3128--3139
R. Bompis and
E. Gobet Stochastic Approximation Finite Element
Method: Analytical Formulas for
Multidimensional Diffusion Process . . . 3140--3164
Fleurianne Bertrand and
Steffen Münzenmaier and
Gerhard Starke First-order System Least Squares on
Curved Boundaries: Higher-order
Raviart--Thomas Elements . . . . . . . . 3165--3180
Assyr Abdulle and
Gilles Vilmart and
Konstantinos C. Zygalakis Long Time Accuracy of Lie--Trotter
Splitting Methods for Langevin Dynamics 1--16
Adrian Sandu and
Michael Günther A Generalized-Structure Approach to
Additive Runge--Kutta Methods . . . . . 17--42
Carsten Carstensen and
Eun-Jae Park Convergence and Optimality of Adaptive
Least Squares Finite Element Methods . . 43--62
Jong Ho Lee A Balancing Domain Decomposition by
Constraints Deluxe Method for
Reissner--Mindlin Plates with Falk--Tu
Elements . . . . . . . . . . . . . . . . 63--81
Jeff Calder and
Selim Esedo\uglu and
Alfred O. Hero A PDE-based Approach to Nondominated
Sorting . . . . . . . . . . . . . . . . 82--104
Takahito Kashiwabara and
Claudia Maria Colciago and
Luca Ded\`e and
Alfio Quarteroni Well-Posedness, Regularity, and
Convergence Analysis of the Finite
Element Approximation of a Generalized
Robin Boundary Value Problem . . . . . . 105--126
Amanda E. Diegel and
Xiaobing H. Feng and
Steven M. Wise Analysis of a Mixed Finite Element
Method for a
Cahn--Hilliard--Darcy--Stokes System . . 127--152
Zhongqiang Zhang and
Michael V. Tretyakov and
Boris Rozovskii and
George E. Karniadakis Wiener Chaos Versus Stochastic
Collocation Methods for Linear
Advection--Diffusion-Reaction Equations
with Multiplicative White Noise . . . . 153--183
Zhonghua Qiao and
Tao Tang and
Hehu Xie Error Analysis of a Mixed Finite Element
Method for the Molecular Beam Epitaxy
Model . . . . . . . . . . . . . . . . . 184--205
Haijin Wang and
Chi-Wang Shu and
Qiang Zhang Stability and Error Estimates of Local
Discontinuous Galerkin Methods with
Implicit---Explicit Time-Marching for
Advection--Diffusion Problems . . . . . 206--227
Adérito Araújo and
Sílvia Barbeiro and
Pedro Serranho Convergence of Finite Difference Schemes
for Nonlinear Complex Reaction-Diffusion
Processes . . . . . . . . . . . . . . . 228--250
Eugene C. Gartland, Jr. and
Alison Ramage A Renormalized Newton Method for Liquid
Crystal Director Modeling . . . . . . . 251--278
Jie Shen and
Xiaofeng Yang Decoupled, Energy Stable Schemes for
Phase-Field Models of Two-Phase
Incompressible Flows . . . . . . . . . . 279--296
A. Klawonn and
P. Radtke and
O. Rheinbach FETI--DP Methods with an Adaptive Coarse
Space . . . . . . . . . . . . . . . . . 297--320
Evgeniy Zharovsky and
Adrian Sandu and
Hong Zhang A Class Of Implicit-Explicit Two-Step
Runge--Kutta Methods . . . . . . . . . . 321--341
Yalchin Efendiev and
Raytcho Lazarov and
Ke Shi A Multiscale HDG Method for Second Order
Elliptic Equations. Part I. Polynomial
and Homogenization-Based Multiscale
Spaces . . . . . . . . . . . . . . . . . 342--369
Xuerong Mao Almost Sure Exponential Stability in the
Numerical Simulation of Stochastic
Differential Equations . . . . . . . . . 370--389
T. Nikazad and
M. Abbasi Perturbation-Resilient Iterative Methods
with an Infinite Pool of Mappings . . . 390--404
Zhiqiang Cai and
Rob Falgout and
Shun Zhang Div First-Order System LL* (FOSLL*) for
Second-Order Elliptic Partial
Differential Equations . . . . . . . . . 405--420
Kristian Bredies and
Hongpeng Sun Preconditioned Douglas--Rachford
Splitting Methods for Convex-concave
Saddle-point Problems . . . . . . . . . 421--444
Roland Becker and
Melanie Bittl and
Dmitri Kuzmin Analysis of a Combined CG1--DG2 Method
for the Transport Equation . . . . . . . 445--463
Georgios Akrivis Stability of Implicit-Explicit Backward
Difference Formulas For Nonlinear
Parabolic Equations . . . . . . . . . . 464--484
Marlis Hochbruck and
Tomislav Pazur Implicit Runge--Kutta Methods and
Discontinuous Galerkin Discretizations
for Linear Maxwell's Equations . . . . . 485--507
Paul Deuring and
Robert Eymard and
Marcus Mildner $ L^2 $-Stability Independent of
Diffusion for a Finite Element--Finite
Volume Discretization of a Linear
Convection--Diffusion Equation . . . . . 508--526
Mikaël Barboteu and
Krzysztof Bartosz and
Weimin Han and
Tomasz Janiczko Numerical Analysis of a Hyperbolic
Hemivariational Inequality Arising in
Dynamic Contact . . . . . . . . . . . . 527--550
Dominic Breit and
Lars Diening and
Sebastian Schwarzacher Finite Element Approximation of the $
p(\cdot)$-Laplacian . . . . . . . . . . 551--572
Martin J. Gander and
Soheil Hajian Analysis of Schwarz Methods for a
Hybridizable Discontinuous Galerkin
Discretization . . . . . . . . . . . . . 573--597
Paola F. Antonietti and
Marco Sarti and
Marco Verani Multigrid Algorithms for $ h
p$-Discontinuous Galerkin
Discretizations of Elliptic Problems . . 598--618
Xiangfan Piao and
SangDong Kim and
Philsu Kim and
Jae-Min Kwon and
Dokkyun Yi An Iteration Free Backward
Semi-Lagrangian Scheme for Guiding
Center Problems . . . . . . . . . . . . 619--643
Andreas Weinmann and
Martin Storath and
Laurent Demaret The $ L^1 $-Potts Functional for Robust
Jump-Sparse Reconstruction . . . . . . . 644--673
Jan Ernest and
Philippe G. LeFloch and
Siddhartha Mishra Schemes with Well-Controlled Dissipation 674--699
Cesáreo González and
Mechthild Thalhammer Higher-Order Exponential Integrators for
Quasi-Linear Parabolic Problems. Part I:
Stability . . . . . . . . . . . . . . . 701--719
Xuemin Tu and
Jing Li A FETI-DP Type Domain Decomposition
Algorithm for Three-Dimensional
Incompressible Stokes Equations . . . . 720--742
Kinjal Basu and
Art B. Owen Low Discrepancy Constructions in the
Triangle . . . . . . . . . . . . . . . . 743--761
Xiaochuan Tian and
Qiang Du Nonconforming Discontinuous Galerkin
Methods for Nonlocal Variational
Problems . . . . . . . . . . . . . . . . 762--781
Yu Du and
Haijun Wu Preasymptotic Error Analysis of Higher
Order FEM and CIP--FEM for Helmholtz
Equation with High Wave Number . . . . . 782--804
Alex Toth and
C. T. Kelley Convergence Analysis for Anderson
Acceleration . . . . . . . . . . . . . . 805--819
S. V. Pereverzyev and
I. H. Sloan and
P. Tkachenko Parameter Choice Strategies for
Least-squares Approximation of Noisy
Smooth Functions on the Sphere . . . . . 820--835
Coralia Cartis and
Nicholas I. M. Gould and
Philippe L. Toint On the Evaluation Complexity of
Constrained Nonlinear Least-Squares and
General Constrained Nonlinear
Optimization Using Second-Order Methods 836--851
Michael Griebel and
Christian Rieger and
Barbara Zwicknagl Multiscale Approximation and Reproducing
Kernel Hilbert Space Methods . . . . . . 852--873
C. Carstensen and
D. J. Liu Nonconforming FEMs for an Optimal Design
Problem . . . . . . . . . . . . . . . . 874--894
François James and
Nicolas Vauchelet Numerical Methods for One-Dimensional
Aggregation Equations . . . . . . . . . 895--916
Christian Lubich and
Ivan V. Oseledets and
Bart Vandereycken Time Integration of Tensor Trains . . . 917--941
Waixiang Cao and
Zhimin Zhang and
Qingsong Zou Is $ 2 k$-Conjecture Valid for Finite
Volume Methods? . . . . . . . . . . . . 942--962
Aekta Aggarwal and
Rinaldo M. Colombo and
Paola Goatin Nonlocal Systems of Conservation Laws in
Several Space Dimensions . . . . . . . . 963--983
Walter Zulehner The Ciarlet--Raviart Method for
Biharmonic Problems on General Polygonal
Domains: Mapping Properties and
Preconditioning . . . . . . . . . . . . 984--1004
Volker John and
Julia Novo Analysis of the Pressure Stabilized
Petrov--Galerkin Method for the
Evolutionary Stokes Equations Avoiding
Time Step Restrictions . . . . . . . . . 1005--1031
Yuan-Ming Wang Fourth-Order Compact Finite Difference
Methods and Monotone Iterative
Algorithms for Quasi-Linear Elliptic
Boundary Value Problems . . . . . . . . 1032--1057
Alexandre Ern and
Martin Vohralík Polynomial-Degree-Robust A Posteriori
Estimates in a Unified Setting for
Conforming, Nonconforming, Discontinuous
Galerkin, and Mixed Discretizations . . 1058--1081
Ludwig Gauckler Error Analysis of Trigonometric
Integrators for Semilinear Wave
Equations . . . . . . . . . . . . . . . 1082--1106
Mark Ainsworth and
Gabriel R. Barrenechea and
Andreas Wachtel Stabilization of High Aspect Ratio Mixed
Finite Elements for Incompressible Flow 1107--1120
Tao Lin and
Yanping Lin and
Xu Zhang Partially Penalized Immersed Finite
Element Methods For Elliptic Interface
Problems . . . . . . . . . . . . . . . . 1121--1144
Paola F. Antonietti and
Andreas Dedner and
Pravin Madhavan and
Simone Stangalino and
Björn Stinner and
Marco Verani High Order Discontinuous Galerkin
Methods for Elliptic Problems on
Surfaces . . . . . . . . . . . . . . . . 1145--1171
Jean-François Chassagneux and
Adrien Richou Numerical Stability Analysis of the
Euler Scheme for BSDEs . . . . . . . . . 1172--1193
Peyman Hessari Pseudospectral Least Squares Method for
Stokes--Darcy Equations . . . . . . . . 1195--1213
R. R. Lederman and
V. Rokhlin On the Analytical and Numerical
Properties of the Truncated Laplace
Transform I . . . . . . . . . . . . . . 1214--1235
Jörg Grande Finite Element Discretization Error
Analysis of a General Interfacial Stress
Functional . . . . . . . . . . . . . . . 1236--1255
Christine Bernardi and
Tomás Chacón Rebollo and
Driss Yakoubi Finite Element Discretization of the
Stokes and Navier--Stokes Equations with
Boundary Conditions on the Pressure . . 1256--1279
Jan Giesselmann and
Charalambos Makridakis and
Tristan Pryer A Posteriori Analysis of Discontinuous
Galerkin Schemes for Systems of
Hyperbolic Conservation Laws . . . . . . 1280--1303
Roland Herzog and
Ekkehard Sachs Superlinear Convergence of Krylov
Subspace Methods for Self-Adjoint
Problems in Hilbert Space . . . . . . . 1304--1324
Jianjun Liu and
Liqun Cao and
Ningning Yan and
Junzhi Cui Multiscale Approach for Optimal Design
in Conductivity of Composite Materials 1325--1349
Roberto Garrappa Numerical Evaluation of Two and Three
Parameter Mittag-Leffler Functions . . . 1350--1369
Constantin Bacuta and
Matthew E. Hassell and
George C. Hsiao and
Francisco-Javier Sayas Boundary Integral Solvers for an
Evolutionary Exterior Stokes Problem . . 1370--1392
Hailiang Liu and
Wenli Cai and
Ning Su Entropy Satisfying Schemes for Computing
Selection Dynamics in Competitive
Interactions . . . . . . . . . . . . . . 1393--1417
Buyang Li and
Weiwei Sun Regularity of the Diffusion-Dispersion
Tensor and Error Analysis of Galerkin
FEMs for a Porous Medium Flow . . . . . 1418--1437
Jun Hu A New Family of Efficient Conforming
Mixed Finite Elements on Both
Rectangular and Cuboid Meshes for Linear
Elasticity in the Symmetric Formulation 1438--1463
P. Kuberry and
H. Lee Analysis of a Fluid-Structure
Interaction Problem Recast in an Optimal
Control Setting . . . . . . . . . . . . 1464--1487
Guillaume Drouet and
Patrick Hild Optimal Convergence for Discrete
Variational Inequalities Modelling
Signorini Contact in $2$D and $3$D
without Additional Assumptions on the
Unknown Contact Set . . . . . . . . . . 1488--1507
G. Zhang and
C. Webster and
M. Gunzburger and
J. Burkardt A Hyperspherical Adaptive Sparse-Grid
Method for High-Dimensional
Discontinuity Detection . . . . . . . . 1508--1536
Seungil Kim and
Hui Zhang Optimized Schwarz Method with Complete
Radiation Transmission Conditions for
the Helmholtz Equation in Waveguides . . 1537--1558
Gaël Poëtte and
Alexandre Birolleau and
Didier Lucor Iterative Polynomial Approximation
Adapting to Arbitrary Probability
Distribution . . . . . . . . . . . . . . 1559--1584
Zhoufeng Wang and
Gang Bao and
Jiaqing Li and
Peijun Li and
Haijun Wu An Adaptive Finite Element Method for
the Diffraction Grating Problem with
Transparent Boundary Condition . . . . . 1585--1607
Gang Bao and
Shuai Lu and
William Rundell and
Boxi Xu A Recursive Algorithm for MultiFrequency
Acoustic Inverse Source Problems . . . . 1608--1628
Chunmei Su and
Zhiping Li Error Analysis of a Dual-parametric
Bi-quadratic FEM in Cavitation
Computation in Elasticity . . . . . . . 1629--1649
Waixiang Cao and
Chi-Wang Shu and
Yang Yang and
Zhimin Zhang Superconvergence of Discontinuous
Galerkin Methods for Two-Dimensional
Hyperbolic Equations . . . . . . . . . . 1651--1671
Jitendra Kumar and
Jitraj Saha and
Evangelos Tsotsas Development and Convergence Analysis of
a Finite Volume Scheme for Solving
Breakage Equation . . . . . . . . . . . 1672--1689
Florent Renac Stationary Discrete Shock Profiles for
Scalar Conservation Laws with a
Discontinuous Galerkin Method . . . . . 1690--1715
Zhong-Zhi Bai and
Miroslav RozloznÍk On the Numerical Behavior of Matrix
Splitting Iteration Methods for Solving
Linear Systems . . . . . . . . . . . . . 1716--1737
Jeffrey Willert and
Xiaojun Chen and
C. T. Kelley Newton's Method for Monte Carlo--Based
Residuals . . . . . . . . . . . . . . . 1738--1757
Xin Liu and
Zaiwen Wen and
Xiao Wang and
Michael Ulbrich and
Yaxiang Yuan On the Analysis of the Discretized
Kohn--Sham Density Functional Theory . . 1758--1785
Weiguo Gao and
Jing Leng and
Xiang Zhou An Iterative Minimization Formulation
for Saddle Point Search . . . . . . . . 1786--1805
Peter Hansbo and
Mats G. Larson and
Sara Zahedi Stabilized Finite Element Approximation
of the Mean Curvature Vector on Closed
Surfaces . . . . . . . . . . . . . . . . 1806--1832
Andrew J. Christlieb and
Yaman Güçlü and
David C. Seal The Picard Integral Formulation of
Weighted Essentially Nonoscillatory
Schemes . . . . . . . . . . . . . . . . 1833--1856
J. Zudrop and
J. S. Hesthaven Accuracy of High Order and Spectral
Methods for Hyperbolic Conservation Laws
with Discontinuous Solutions . . . . . . 1857--1875
F. Guillén González and
J. R. Rodríguez Galván Stabilized Schemes for the Hydrostatic
Stokes Equations . . . . . . . . . . . . 1876--1896
Alex Townsend A Fast Analysis-Based Discrete Hankel
Transform Using Asymptotic Expansions 1897--1917
Jiaxiang Cai and
Jialin Hong and
Yushun Wang and
Yuezheng Gong Two Energy-Conserved Splitting Methods
for Three-Dimensional Time-Domain
Maxwell's Equations and the Convergence
Analysis . . . . . . . . . . . . . . . . 1918--1940
Hongxing Rui and
Wei Liu A Two-Grid Block-Centered Finite
Difference Method For Darcy--Forchheimer
Flow in Porous Media . . . . . . . . . . 1941--1962
Rajib Dutta and
Ujjwal Koley and
Nils Henrik Risebro Convergence of a Higher Order Scheme for
the Korteweg--de Vries Equation . . . . 1963--1983
Lin Zhao and
Alex Barnett Robust and Efficient Solution of the
Drum Problem via Nyström Approximation of
the Fredholm Determinant . . . . . . . . 1984--2007
Alina Chertock and
Shumo Cui and
Alexander Kurganov and
Tong Wu Steady State and Sign Preserving
Semi-Implicit Runge--Kutta Methods for
ODEs with Stiff Damping Term . . . . . . 2008--2029
Yanping Lin and
Min Yang and
Qingsong Zou $ L^2 $ Error Estimates for a Class of
Any Order Finite Volume Schemes Over
Quadrilateral Meshes . . . . . . . . . . 2030--2050
Thanh Hai Ong and
Thi Thao Phuong Hoang and
Stéphane P. A. Bordas and
H. Nguyen-Xuan A Staggered Cell-Centered Finite Element
Method for Compressible and
Nearly-Incompressible Linear Elasticity
on General Meshes . . . . . . . . . . . 2051--2073
Zhongqiang Zhang and
Fanhai Zeng and
George Em Karniadakis Optimal Error Estimates of Spectral
Petrov--Galerkin and Collocation Methods
for Initial Value Problems of Fractional
Differential Equations . . . . . . . . . 2074--2096
J. Thomas Beale Uniform Error Estimates for
Navier--Stokes Flow with an Exact Moving
Boundary Using the Immersed Interface
Method . . . . . . . . . . . . . . . . . 2097--2111
Bertram Düring and
Christof Heuer High-Order Compact Schemes for Parabolic
Problems with Mixed Derivatives in
Multiple Space Dimensions . . . . . . . 2113--2134
Daniele A. Di Pietro and
Jérôme Droniou and
Alexandre Ern A Discontinuous-Skeletal Method for
Advection--Diffusion-Reaction on General
Meshes . . . . . . . . . . . . . . . . . 2135--2157
Ken'ichiro Tanaka and
Alexis Akira Toda Discretizing Distributions with Exact
Moments: Error Estimate and Convergence
Analysis . . . . . . . . . . . . . . . . 2158--2177
Julian Fischer A Posteriori Modeling Error Estimates
for the Assumption of Perfect
Incompressibility in the Navier--Stokes
Equation . . . . . . . . . . . . . . . . 2178--2205
F. M. Hante and
M. S. Mommer and
A. Potschka Newton--Picard Preconditioners for
Time-Periodic Parabolic Optimal Control
Problems . . . . . . . . . . . . . . . . 2206--2225
J. H. Adler and
T. J. Atherton and
D. B. Emerson and
S. P. MacLachlan An Energy-Minimization Finite-Element
Approach for the Frank--Oseen Model of
Nematic Liquid Crystals . . . . . . . . 2226--2254
B. J. Grieshaber and
A. T. McBride and
B. D. Reddy Uniformly Convergent Interior Penalty
Methods Using Multilinear Approximations
for Problems in Elasticity . . . . . . . 2255--2278
Harbir Antil and
Ricardo H. Nochetto and
Patrick Sodré Optimal Control of a Free Boundary
Problem with Surface Tension Effects: a
Priori Error Analysis . . . . . . . . . 2279--2306
Boris Houska and
Mario E. Villanueva and
BenoÎt Chachuat Stable Set-Valued Integration of
Nonlinear Dynamic Systems using Affine
Set-Parameterizations . . . . . . . . . 2307--2328
Jeffrey Humpherys and
Joshua Lytle Root Following in Evans Function
Computation . . . . . . . . . . . . . . 2329--2346
Fotios Kasolis and
Eddie Wadbro and
Martin Berggren Analysis of Fictitious Domain
Approximations of Hard Scatterers . . . 2347--2362
P. Bochev and
M. Perego and
K. Peterson Formulation and Analysis of a
Parameter-Free Stabilized Finite Element
Method . . . . . . . . . . . . . . . . . 2363--2388
Qinian Jin Inexact Newton--Landweber Iteration in
Banach Spaces with NonSmooth Convex
Penalty Terms . . . . . . . . . . . . . 2389--2413
S. Sauter and
J. Zech A Posteriori Error Estimation of $ h
p$-$ d G$ Finite Element Methods for
Highly Indefinite Helmholtz Problems . . 2414--2440
R. Bélanger-Rioux and
L. Demanet Compressed Absorbing Boundary Conditions
via Matrix Probing . . . . . . . . . . . 2441--2471
John Maclean A Note on Implementations of the
Boosting Algorithm and Heterogeneous
Multiscale Methods . . . . . . . . . . . 2472--2487
Zhijian He and
Xiaoqun Wang On the Convergence Rate of Randomized
Quasi-Monte Carlo for Discontinuous
Functions . . . . . . . . . . . . . . . 2488--2503
S. Sato and
T. Matsuo and
H. Suzuki and
D. Furihata A Lyapunov-Type Theorem for Dissipative
Numerical Integrators with Adaptive
Time-Stepping . . . . . . . . . . . . . 2505--2518
Natalia Kopteva Maximum-Norm A Posteriori Error
Estimates for Singularly Perturbed
Reaction-Diffusion Problems on
Anisotropic Meshes . . . . . . . . . . . 2519--2544
D. P. Bourne and
S. M. Roper Centroidal Power Diagrams, Lloyd's
Algorithm, and Applications to Optimal
Location Problems . . . . . . . . . . . 2545--2569
Shoufu Li and
Yunfei Li $B$-Convergence Theory of Runge--Kutta
Methods for Stiff Volterra Functional
Differential Equations with Infinite
Integration Interval . . . . . . . . . . 2570--2583
Daniele Boffi and
Nicola Cavallini and
Lucia Gastaldi The Finite Element Immersed Boundary
Method with Distributed Lagrange
Multiplier . . . . . . . . . . . . . . . 2584--2604
Jan Martin Nordbotten Convergence of a Cell-Centered Finite
Volume Discretization for Linear
Elasticity . . . . . . . . . . . . . . . 2605--2625
Rolf Stenberg and
Juha Videman On the Error Analysis of Stabilized
Finite Element Methods for the Stokes
Problem . . . . . . . . . . . . . . . . 2626--2633
Stefan Takacs A Robust Multigrid Method for the
Time-Dependent Stokes Problem . . . . . 2634--2654
Stefan Engblom Strong Convergence for Split-Step
Methods in Stochastic Jump Kinetics . . 2655--2676
Lijun Yi and
Benqi Guo An $h$--$p$ Version of the Continuous
Petrov--Galerkin Finite Element Method
for Volterra Integro-Differential
Equations with Smooth and Nonsmooth
Kernels . . . . . . . . . . . . . . . . 2677--2704
Daniel Appelö and
Thomas Hagstrom A New Discontinuous Galerkin Formulation
for Wave Equations in Second-Order Form 2705--2726
Shishun Li and
Xiao-Chuan Cai Convergence Analysis of Two-Level
Space--time Additive Schwarz Method for
Parabolic Equations . . . . . . . . . . 2727--2751
Victor D. Didenko and
Tao Tang and
Anh My Vu Spline Galerkin Methods for the
Sherman--Lauricella Equation on Contours
with Corners . . . . . . . . . . . . . . 2752--2770
S. Maset The Collocation Method in the Numerical
Solution of Boundary Value Problems for
Neutral Functional Differential
Equations. Part I: Convergence Results 2771--2793
S. Maset The Collocation Method in the Numerical
Solution of Boundary Value Problems for
Neutral Functional Differential
Equations. Part II: Differential
Equations with Deviating Arguments . . . 2794--2821
Evan S. Gawlik and
Adrian J. Lew Unified Analysis of Finite Element
Methods for Problems with Moving
Boundaries . . . . . . . . . . . . . . . 2822--2846
Pauline Lafitte and
Annelies Lejon and
Giovanni Samaey A High-Order Asymptotic-Preserving
Scheme for Kinetic Equations Using
Projective Integration . . . . . . . . . 1--33
P. F. Antonietti and
L. Beiraño da Veiga and
S. Scacchi and
M. Verani A $ C^1 $ Virtual Element Method for the
Cahn--Hilliard Equation with Polygonal
Meshes . . . . . . . . . . . . . . . . . 34--56
Jean-Luc Guermond and
Bojan Popov Error Estimates of a First-order
Lagrange Finite Element Technique for
Nonlinear Scalar Conservation Equations 57--85
Andy T. S. Wan and
Alexander Bihlo and
Jean-Christophe Nave The Multiplier Method to Construct
Conservative Finite Difference Schemes
for Ordinary and Partial Differential
Equations . . . . . . . . . . . . . . . 86--119
Emmanuil H. Georgoulis and
Omar Lakkis and
Charalambos G. Makridakis and
Juha M. Virtanen A Posteriori Error Estimates for
Leap-Frog and Cosine Methods for Second
Order Evolution Problems . . . . . . . . 120--136
Martin Campos Pinto and
Frédérique Charles Uniform Convergence of a Linearly
Transformed Particle Method for the
Vlasov--Poisson System . . . . . . . . . 137--160
Yves Achdou and
Alessio Porretta Convergence of a Finite Difference
Scheme to Weak Solutions of the System
of Partial Differential Equations
Arising in Mean Field Games . . . . . . 161--186
Florent Renac Stability Analysis of Discontinuous
Galerkin Discrete Shock Profiles for
Steady Scalar Conservation Laws . . . . 187--209
Beniamin Bogosel and
Bozhidar Velichkov A Multiphase Shape Optimization Problem
for Eigenvalues: Qualitative Study and
Numerical Results . . . . . . . . . . . 210--241
Stefano Berrone and
Andrea Borio and
Stefano Scial\`o A Posteriori Error Estimate for a
PDE-Constrained Optimization Formulation
for the Flow in DFNs . . . . . . . . . . 242--261
Volker Michel and
Roger Telschow The Regularized Orthogonal Functional
Matching Pursuit for Ill-Posed Inverse
Problems . . . . . . . . . . . . . . . . 262--287
Thi-Thao-Phuong Hoang and
Caroline Japhet and
Michel Kern and
Jean E. Roberts Space-Time Domain Decomposition for
Reduced Fracture Models in Mixed
Formulation . . . . . . . . . . . . . . 288--316
Francesca Tantardini and
Andreas Veeser The $ L^2 $-Projection and
Quasi-Optimality of Galerkin Methods for
Parabolic Equations . . . . . . . . . . 317--340
Claudia König and
Frank Werner and
Thorsten Hohage Convergence Rates for Exponentially
Ill-Posed Inverse Problems with
Impulsive Noise . . . . . . . . . . . . 341--360
Andreas Potschka Backward Step Control for Global
Newton-Type Methods . . . . . . . . . . 361--387
Jörg Grande and
Arnold Reusken A Higher Order Finite Element Method for
Partial Differential Equations on
Surfaces . . . . . . . . . . . . . . . . 388--414
Muruhan Rathinam Convergence of Moments of tau Leaping
Schemes for Unbounded Markov Processes
on Integer Lattices . . . . . . . . . . 415--439
Kerstin Küpper and
Martin Frank and
Shi Jin An Asymptotic Preserving Two-dimensional
Staggered Grid Method for Multiscale
Transport Equations . . . . . . . . . . 440--461
Libin Jiao and
Bo Dong and
Jintao Zhang and
Bo Yu Polynomial Homotopy Method for the
Sparse Interpolation Problem. Part I:
Equally Spaced Sampling . . . . . . . . 462--480
Bangti Jin and
Raytcho Lazarov and
Zhi Zhou A Petrov--Galerkin Finite Element Method
for Fractional Convection--Diffusion
Equations . . . . . . . . . . . . . . . 481--503
David F. Anderson and
Desmond J. Higham and
Yu Sun Multilevel Monte Carlo for Stochastic
Differential Equations with Small Noise 505--529
Qinghai Zhang and
Aaron Fogelson MARS: an Analytic Framework of Interface
Tracking via Mapping and Adjusting
Regular Semialgebraic Sets . . . . . . . 530--560
Dmitriy Leykekhman and
Boris Vexler Finite Element Pointwise Results on
Convex Polyhedral Domains . . . . . . . 561--587
G. M. Coclite and
O. Reichmann and
N. H. Risebro A Convergent Difference Scheme for a
Class of Partial Integro-Differential
Equations Modeling Pricing under
Uncertainty . . . . . . . . . . . . . . 588--605
S. Chen and
F. Liu and
X. Jiang and
I. Turner and
K. Burrage Fast Finite Difference Approximation for
Identifying Parameters in a
Two-dimensional Space-fractional
Nonlocal Model with Variable Diffusivity
Coefficients . . . . . . . . . . . . . . 606--624
Wei Hong Yang and
Deren Han Linear Convergence of the Alternating
Direction Method of Multipliers for a
Class of Convex Optimization Problems 625--640
Thomas Rey and
Changhui Tan An Exact Rescaling Velocity Method for
some Kinetic Flocking Models . . . . . . 641--664
R. R. Lederman and
V. Rokhlin On the Analytical and Numerical
Properties of the Truncated Laplace
Transform. Part II . . . . . . . . . . . 665--687
Roland Herzog and
Susann Mach Preconditioned Solution of State
Gradient Constrained Elliptic Optimal
Control Problems . . . . . . . . . . . . 688--718
Vanni Noferini and
Alex Townsend Numerical Instability of Resultant
Methods for Multidimensional Rootfinding 719--743
Markus Bachmayr and
Wolfgang Dahmen Adaptive Low-Rank Methods: Problems on
Sobolev Spaces . . . . . . . . . . . . . 744--796
Michael S. Floater and
Ming-Jun Lai Polygonal Spline Spaces and the
Numerical Solution of the Poisson
Equation . . . . . . . . . . . . . . . . 797--824
Xiaobing Feng and
Yukun Li and
Yulong Xing Analysis of Mixed Interior Penalty
Discontinuous Galerkin Methods for the
Cahn--Hilliard Equation and the
Hele--Shaw Flow . . . . . . . . . . . . 825--847
Ricardo H. Nochetto and
Enrique Otárola and
Abner J. Salgado A PDE Approach to Space-Time Fractional
Parabolic Problems . . . . . . . . . . . 848--873
Mohammad Zakerzadeh and
Georg May On the Convergence of a Shock Capturing
Discontinuous Galerkin Method for
Nonlinear Hyperbolic Systems of
Conservation Laws . . . . . . . . . . . 874--898
Ran Zhang and
Hui Liang and
Hermann Brunner Analysis of Collocation Methods for
Generalized Auto-Convolution Volterra
Integral Equations . . . . . . . . . . . 899--920
M. Dambrine and
I. Greff and
H. Harbrecht and
B. Puig Numerical Solution of the Poisson
Equation on Domains with a Thin Layer of
Random Thickness . . . . . . . . . . . . 921--941
Jan Martin Nordbotten Stable Cell-Centered Finite Volume
Discretization for Biot Equations . . . 942--968
Mario Ullrich and
Tino Ullrich The Role of Frolov's Cubature Formula
for Functions with Bounded Mixed
Derivative . . . . . . . . . . . . . . . 969--993
T. Chacón Rebollo and
V. Girault and
F. Murat and
O. Pironneau Analysis of a Coupled Fluid-Structure
Model with Applications to Hemodynamics 994--1019
Emil Kieri and
Christian Lubich and
Hanna Walach Discretized Dynamical Low-Rank
Approximation in the Presence of Small
Singular Values . . . . . . . . . . . . 1020--1038
Marco Discacciati and
Paola Gervasio and
Alessandro Giacomini and
Alfio Quarteroni The Interface Control Domain
Decomposition Method for Stokes--Darcy
Coupling . . . . . . . . . . . . . . . . 1039--1068
Jessika Camanño and
Gabriel N. Gatica and
Ricardo Oyarzúa and
Giordano Tierra An Augmented Mixed Finite Element Method
for the Navier--Stokes Equations with
Variable Viscosity . . . . . . . . . . . 1069--1092
Rikard Anton and
David Cohen and
Stig Larsson and
Xiaojie Wang Full Discretization of Semilinear
Stochastic Wave Equations Driven by
Multiplicative Noise . . . . . . . . . . 1093--1119
Francis Filbet and
Luis Miguel Rodrigues Asymptotically Stable Particle-In-Cell
Methods for the Vlasov--Poisson System
with a Strong External Magnetic Field 1120--1146
Binjie Li and
Xiaoping Xie BPX Preconditioner for Nonstandard
Finite Element Methods for Diffusion
Problems . . . . . . . . . . . . . . . . 1147--1168
René Schneider and
Gerd Wachsmuth A Posteriori Error Estimation for
Control-Constrained, Linear-Quadratic
Optimal Control Problems . . . . . . . . 1169--1192
Huoyuan Duan and
Ping Lin and
Roger C. E. Tan A Finite Element Method for a
Curlcurl--Graddiv Eigenvalue Interface
Problem . . . . . . . . . . . . . . . . 1193--1228
Wei Gong and
Ningning Yan Finite Element Approximations of
Parabolic Optimal Control Problems with
Controls Acting on a Lower Dimensional
Manifold . . . . . . . . . . . . . . . . 1229--1262
Clément Canc\`es and
Hél\`ene Mathis and
Nicolas Seguin Error Estimate for Time-Explicit Finite
Volume Approximation of Strong Solutions
to Systems of Conservation Laws . . . . 1263--1287
Christopher Keim and
Holger Wendland A High-Order, Analytically
Divergence-Free Approximation Method for
the Time-Dependent Stokes Problem . . . 1288--1312
Praveen Chandrashekar and
Christian Klingenberg Entropy Stable Finite Volume Scheme for
Ideal Compressible MHD on $2$-D
Cartesian Meshes . . . . . . . . . . . . 1313--1340
P. Azimzadeh and
P. A. Forsyth Weakly Chained Matrices, Policy
Iteration, and Impulse Control . . . . . 1341--1364
Dmitriy Leykekhman and
Boris Vexler Pointwise Best Approximation Results for
Galerkin Finite Element Solutions of
Parabolic Problems . . . . . . . . . . . 1365--1384
Martin Halla Convergence of Hardy Space Infinite
Elements for Helmholtz Scattering and
Resonance Problems . . . . . . . . . . . 1385--1400
Dang-Manh Nguyen and
Jörg Peters Nonuniform Discontinuous Galerkin
Filters via Shift and Scale . . . . . . 1401--1422
Michael Feischl and
Dirk Praetorius and
Kristoffer G. van der Zee An Abstract Analysis of Optimal
Goal-Oriented Adaptivity . . . . . . . . 1423--1448
Christian Bayer and
Peter K. Friz and
Sebastian Riedel and
John Schoenmakers From Rough Path Estimates to Multilevel
Monte Carlo . . . . . . . . . . . . . . 1449--1483
Magnus Svärd A Convergent Numerical Scheme for the
Compressible Navier--Stokes Equations 1484--1506
Assyr Abdulle and
Timothée Pouchon A Priori Error Analysis of the Finite
Element Heterogeneous Multiscale Method
for the Wave Equation over Long Time . . 1507--1534
William W. Hager and
Maryam Yashtini and
Hongchao Zhang An $ \mathcal O(1 / k) $ Convergence
Rate for the Variable Stepsize Bregman
Operator Splitting Algorithm . . . . . . 1535--1556
Haiyong Wang On the Optimal Estimates and Comparison
of Gegenbauer Expansion Coefficients . . 1557--1581
Jean-Marie Mirebeau Minimal Stencils for Discretizations of
Anisotropic PDEs Preserving Causality or
the Maximum Principle . . . . . . . . . 1582--1611
Weizhang Huang and
Lennard Kamenski and
Jens Lang Stability of Explicit One-Step Methods
for P1-Finite Element Approximation of
Linear Diffusion Equations on
Anisotropic Meshes . . . . . . . . . . . 1612--1634
Matthew F. Causley and
Hana Cho and
Andrew J. Christlieb and
David C. Seal Method of Lines Transpose: High Order
$L$-Stable $ {\mathcal O}(N)$ Schemes
for Parabolic Equations Using Successive
Convolution . . . . . . . . . . . . . . 1635--1652
Dong Li and
Zhonghua Qiao and
Tao Tang Characterizing the Stabilization Size
for Semi-Implicit Fourier-Spectral
Method to Phase Field Equations . . . . 1653--1681
François P. Hamon and
Hamdi A. Tchelepi Analysis of Hybrid Upwinding for
Fully-Implicit Simulation of Three-Phase
Flow with Gravity . . . . . . . . . . . 1682--1712
Y. Maday and
O. Mula and
G. Turinici Convergence analysis of the Generalized
Empirical Interpolation Method . . . . . 1713--1731
John W. Barrett and
Harald Garcke and
Robert Nürnberg Computational Parametric Willmore Flow
with Spontaneous Curvature and Area
Difference Elasticity Effects . . . . . 1732--1762
Kim Ngan Le and
William McLean and
Kassem Mustapha Numerical Solution of the
Time-Fractional Fokker--Planck Equation
with General Forcing . . . . . . . . . . 1763--1784
Weizhu Bao and
Yongyong Cai and
Xiaowei Jia and
Qinglin Tang A Uniformly Accurate Multiscale Time
Integrator Pseudospectral Method for the
Dirac Equation in the Nonrelativistic
Limit Regime . . . . . . . . . . . . . . 1785--1812
Håkon Hoel and
Kody J. H. Law and
Raul Tempone Multilevel ensemble Kalman filtering . . 1813--1839
Konstantinos Dareiotis and
Chaman Kumar and
Sotirios Sabanis On Tamed Euler Approximations of SDEs
Driven by Lévy Noise with Applications to
Delay Equations . . . . . . . . . . . . 1840--1872
Florent Chave and
Daniele A. Di Pietro and
Fabien Marche and
Franck Pigeonneau A Hybrid High-Order Method for the
Cahn--Hilliard problem in Mixed Form . . 1873--1898
Qiang Du and
Jiang Yang Asymptotically Compatible Fourier
Spectral Approximations of Nonlocal
Allen--Cahn Equations . . . . . . . . . 1899--1919
Ulrik S. Fjordholm and
Susanne Solem Second-Order Convergence of Monotone
Schemes for Conservation Laws . . . . . 1920--1945
Kinjal Basu and
Art B. Owen Transformations and Hardy--Krause
Variation . . . . . . . . . . . . . . . 1946--1966
Erik Burman and
Friedhelm Schieweck Local CIP Stabilization for Composite
Finite Elements . . . . . . . . . . . . 1967--1992
Yuto Miyatake and
John C. Butcher A Characterization of Energy-Preserving
Methods and the Construction of Parallel
Integrators for Hamiltonian Systems . . 1993--2013
Zhi Zhao and
Xiao-Qing Jin and
Zheng-Jian Bai A Geometric Nonlinear Conjugate Gradient
Method for Stochastic Inverse Eigenvalue
Problems . . . . . . . . . . . . . . . . 2015--2035
Yu--Wen Li and
Xinyuan Wu Functionally Fitted Energy-Preserving
Methods for Solving Oscillatory
Nonlinear Hamiltonian Systems . . . . . 2036--2059
Jin Zhang and
Xiaowei Liu and
Min Yang Optimal Order $ L^2 $ Error Estimate of
SDFEM on Shishkin Triangular Meshes for
Singularly Perturbed
Convection--Diffusion Equations . . . . 2060--2080
Shuhuang Xiang On Interpolation Approximation:
Convergence Rates for Polynomial
Interpolation for Functions of Limited
Regularity . . . . . . . . . . . . . . . 2081--2113
Yuling Jiao and
Qinian Jin and
Xiliang Lu and
Weijie Wang Alternating Direction Method of
Multipliers for Linear Inverse Problems 2114--2137
M. Schedensack A New Discretization for $m$ th-Laplace
Equations with Arbitrary Polynomial
Degrees . . . . . . . . . . . . . . . . 2138--2162
Philipp Morgenstern Globally Structured Three-Dimensional
Analysis-Suitable T-Splines: Definition,
Linear Independence and $m$-graded local
refinement . . . . . . . . . . . . . . . 2163--2186
Benjamin Gess and
Beno\^\it Perthame and
Panagiotis E. Souganidis Semi-discretization for Stochastic
Scalar Conservation Laws with Multiple
Rough Fluxes . . . . . . . . . . . . . . 2187--2209
Iván Area and
Dimitar K. Dimitrov and
Eduardo Godoy and
Vanessa G. Paschoa Approximate Calculation of Sums II:
Gaussian Type Quadrature . . . . . . . . 2210--2227
Christoph Erath and
Dirk Praetorius Adaptive Vertex-Centered Finite Volume
Methods with Convergence Rates . . . . . 2228--2255
Ben Adcock and
Rodrigo B. Platte A Mapped Polynomial Method for
High-Accuracy Approximations on
Arbitrary Grids . . . . . . . . . . . . 2256--2281
Guohui Song and
Jacqueline Davis and
Anne Gelb A High-Dimensional Inverse Frame
Operator Approximation Technique . . . . 2282--2301
Wen-ming He and
Runchang Lin and
Zhimin Zhang Ultraconvergence of Finite Element
Method by Richardson Extrapolation for
Elliptic Problems with Constant
Coefficients . . . . . . . . . . . . . . 2302--2322
E. Bänsch and
A. Brenner A Posteriori Error Estimates for
Pressure-Correction Schemes . . . . . . 2323--2358
Fabian Brunner and
Julian Fischer and
Peter Knabner Analysis of a Modified Second-Order
Mixed Hybrid $ B D M_1 $ Finite Element
Method for Transport Problems in
Divergence Form . . . . . . . . . . . . 2359--2378
Andrea Bonito and
Alan Demlow Convergence and Optimality of
Higher-Order Adaptive Finite Element
Methods for Eigenvalue Clusters . . . . 2379--2388
Sebastian Becker and
Arnulf Jentzen and
Peter E. Kloeden An Exponential Wagner--Platen Type
Scheme for SPDEs . . . . . . . . . . . . 2389--2426
Gabriel R. Barrenechea and
Volker John and
Petr Knobloch Analysis of Algebraic Flux Correction
Schemes . . . . . . . . . . . . . . . . 2427--2451
Georg May and
Mohammad Zakerzadeh On the Convergence of Space-Time
Discontinuous Galerkin Schemes for
Scalar Conservation Laws . . . . . . . . 2452--2465
Jean-Luc Guermond and
Bojan Popov Invariant Domains and First-Order
Continuous Finite Element Approximation
for Hyperbolic Systems . . . . . . . . . 2466--2489
M. J. Piggott and
V. Solo Geometric Euler--Maruyama Schemes for
Stochastic Differential Equations in
SO(n) and SE(n) . . . . . . . . . . . . 2490--2516
Mark S. Gockenbach Generalizing the GSVD . . . . . . . . . 2517--2540
Josef Dick and
Frances Y. Kuo and
Quoc T. Le Gia and
Christoph Schwab Multilevel Higher Order QMC
Petrov--Galerkin Discretization for
Affine Parametric Operator Equations . . 2541--2568
Chuchu Chen and
Jialin Hong Symplectic Runge--Kutta
Semidiscretization for Stochastic
Schrödinger Equation . . . . . . . . . . 2569--2593
Barbara Kaltenbacher Regularization Based on All-At-Once
Formulations for Inverse Problems . . . 2594--2618
Enrique Otárola and
Abner J. Salgado Finite Element Approximation of the
Parabolic Fractional Obstacle Problem 2619--2639
Hui Liang and
Hermann Brunner Integral-Algebraic Equations: Theory of
Collocation Methods II . . . . . . . . . 2640--2663
Takashi Goda and
Kosuke Suzuki and
Takehito Yoshiki An Explicit Construction of Optimal
Order Quasi-Monte Carlo Rules for Smooth
Integrands . . . . . . . . . . . . . . . 2664--2683
Roland Becker and
Daniela Capatina and
Robert Luce Local Flux Reconstructions for Standard
Finite Element Methods on Triangular
Meshes . . . . . . . . . . . . . . . . . 2684--2706
Christoph Pflaum and
Rainer Hartmann A Sparse Grid Discretization of the
Helmholtz Equation with Variable
Coefficients in High Dimensions . . . . 2707--2727
Xiang Wang and
Yonghai Li $ L^2 $ Error Estimates for High Order
Finite Volume Methods on Triangular
Meshes . . . . . . . . . . . . . . . . . 2729--2749
Qingguo Hong and
Johannes Kraus Uniformly Stable Discontinuous Galerkin
Discretization and Robust Iterative
Solution Methods for the Brinkman
Problem . . . . . . . . . . . . . . . . 2750--2774
Sofia Lindqvist and
Peder Aursand and
Tore Flåtten and
Anders Aase Solberg Large Time Step TVD Schemes for
Hyperbolic Conservation Laws . . . . . . 2775--2798
Yiannis Hadjimichael and
David I. Ketcheson and
Lajos Lóczi and
Adrián Németh Strong Stability Preserving Explicit
Linear Multistep Methods with Variable
Step Size . . . . . . . . . . . . . . . 2799--2832
Yuhong Zhang and
Yanren Hou and
Li Shan Stability and Convergence Analysis of a
Decoupled Algorithm for a Fluid-Fluid
Interaction Problem . . . . . . . . . . 2833--2867
Cesáreo González and
Mechthild Thalhammer Higher-Order Exponential Integrators for
Quasi-Linear Parabolic Problems. Part
II: Convergence . . . . . . . . . . . . 2868--2888
Manas Rachh and
L. Greengard Integral Equation Methods for Elastance
and Mobility Problems in Two Dimensions 2889--2909
Kartikey Asthana and
Jerry Watkins and
Antony Jameson On the Rate of Convergence of Flux
Reconstruction for Steady-State Problems 2910--2937
WeiPing Shen and
Chong Li and
Jen-Chih Yao Convergence Analysis of Newton-Like
Methods for Inverse Eigenvalue Problems
with Multiple Eigenvalues . . . . . . . 2938--2950
Ricardo Oyarzúa and
Ricardo Ruiz-Baier Locking-Free Finite Element Methods for
Poroelasticity . . . . . . . . . . . . . 2951--2973
Jehanzeb Hameed Chaudhry and
Don Estep and
Simon Tavener and
Varis Carey and
Jeff Sandelin A Posteriori Error Analysis of Two-Stage
Computation Methods with Application to
Efficient Discretization and the
Parareal Algorithm . . . . . . . . . . . 2974--3002
Caroline Moosmüller $ C^1 $ Analysis of Hermite Subdivision
Schemes on Manifolds . . . . . . . . . . 3003--3031
Martina Bukac and
Boris Muha Stability and Convergence Analysis of
the Extensions of the Kinematically
Coupled Scheme for the Fluid--Structure
Interaction . . . . . . . . . . . . . . 3032--3061
Eduard Feireisl and
Radim Hosek and
Martin Michálek A Convergent Numerical Method for the
Full Navier--Stokes--Fourier System in
Smooth Physical Domains . . . . . . . . 3062--3082
Martin Parisot and
Jean-Paul Vila Centered-Potential Regularization for
the Advection Upstream Splitting Method 3083--3104
Todd Arbogast and
Abraham L. Taicher A Linear Degenerate Elliptic Equation
Arising from Two-Phase Mixtures . . . . 3105--3122
Kelong Cheng and
Cheng Wang Long Time Stability of High Order
MultiStep Numerical Schemes for
Two-Dimensional Incompressible
Navier--Stokes Equations . . . . . . . . 3123--3144
Lulu Liu and
David E. Keyes Convergence Analysis for the
Multiplicative Schwarz Preconditioned
Inexact Newton Algorithm . . . . . . . . 3145--3166
Marlis Hochbruck and
Andreas Sturm Error Analysis of a Second-Order Locally
Implicit Method for Linear Maxwell's
Equations . . . . . . . . . . . . . . . 3167--3191
Claudio Canuto and
Ricardo H. Nochetto and
Rob Stevenson and
Marco Verani Adaptive Spectral Galerkin Methods with
Dynamic Marking . . . . . . . . . . . . 3193--3213
M. Paul Laiu and
Cory D. Hauck and
Ryan G. McClarren and
Dianne P. O'Leary and
André L. Tits Positive Filtered $ P_N $ Moment
Closures for Linear Kinetic Equations 3214--3238
A. Alamo and
J. M. Sanz-Serna A Technique for Studying Strong and Weak
Local Errors of Splitting Stochastic
Integrators . . . . . . . . . . . . . . 3239--3257
Paul Leopardi and
Ari Stern The Abstract Hodge--Dirac Operator and
Its Stable Discretization . . . . . . . 3258--3279
Stevan Bellec and
Mathieu Colin and
Mario Ricchiuto Discrete Asymptotic Equations for Long
Wave Propagation . . . . . . . . . . . . 3280--3299
Wanting Xu and
Mihai Anitescu A Limited-Memory Multiple Shooting
Method for Weakly Constrained
Variational Data Assimilation . . . . . 3300--3331
Todd Arbogast and
Maicon R. Correa Two Families of $ H({\rm div}) $ Mixed
Finite Elements on Quadrilaterals of
Minimal Dimension . . . . . . . . . . . 3332--3356
Can Huang and
Yujian Jiao and
Li-Lian Wang and
Zhimin Zhang Optimal Fractional Integration
Preconditioning and Error Analysis of
Fractional Collocation Method Using
Nodal Generalized Jacobi Functions . . . 3357--3387
C. Carstensen and
F. Hellwig Low-Order Discontinuous Petrov--Galerkin
Finite Element Methods for Linear
Elasticity . . . . . . . . . . . . . . . 3388--3410
Andrea Cangiani and
Vitaliy Gyrya and
Gianmarco Manzini The NonConforming Virtual Element Method
for the Stokes Equations . . . . . . . . 3411--3435
Santiago Badia and
Hieu Nguyen Balancing Domain Decomposition by
Constraints and Perturbation . . . . . . 3436--3464
Quentin Mérigot and
Jean-Marie Mirebeau Minimal Geodesics Along
Volume-Preserving Maps, Through
Semidiscrete Optimal Transport . . . . . 3465--3492
Patrick Henning and
Mario Ohlberger and
Barbara Verfürth A New Heterogeneous Multiscale Method
for Time-Harmonic Maxwell's Equations 3493--3522
Andreas Dedner and
Jan Giesselmann A Posteriori Analysis of Fully Discrete
Method of Lines Discontinuous Galerkin
Schemes for Systems of Conservation Laws 3523--3549
Johanna Ridder Convergence of a Finite Difference
Scheme for Two-Dimensional
Incompressible Magnetohydrodynamics . . 3550--3576
Herbert Egger and
Matthias Schlottbom A class of Galerkin Schemes for
Time-Dependent Radiative Transfer . . . 3577--3599
Balázs Kovács and
Buyang Li and
Christian Lubich $A$-Stable Time Discretizations Preserve
Maximal Parabolic Regularity . . . . . . 3600--3624
Thomas Kühn and
Sebastian Mayer and
Tino Ullrich Counting Via Entropy: New Preasymptotics
for the Approximation Numbers of Sobolev
Embeddings . . . . . . . . . . . . . . . 3625--3647
Fleurianne Bertrand and
Gerhard Starke Parametric Raviart--Thomas Elements for
Mixed Methods on Domains with Curved
Surfaces . . . . . . . . . . . . . . . . 3648--3667
Antoine Laurain Stability Analysis of the Reconstruction
Step of the Voronoi Implicit Interface
Method . . . . . . . . . . . . . . . . . 1--30
Marco Donatelli and
Carlo Garoni and
Carla Manni and
Stefano Serra-Capizzano and
Hendrik Speleers Symbol-Based Multigrid Methods for
Galerkin B-Spline Isogeometric Analysis 31--62
Lehel Banjai and
Emmanuil H. Georgoulis and
Oluwaseun Lijoka A Trefftz Polynomial Space--Time
Discontinuous Galerkin Method for the
Second Order Wave Equation . . . . . . . 63--86
Susanne C. Brenner and
Joscha Gedicke and
Li-Yeng Sung and
Yi Zhang An \em A Posteriori Analysis of $ C^0 $
Interior Penalty Methods for the
Obstacle Problem of Clamped Kirchhoff
Plates . . . . . . . . . . . . . . . . . 87--108
Klaus Deckelnick and
Michael Hinze and
Tobias Jordan An Optimal Shape Design Problem for
Plates . . . . . . . . . . . . . . . . . 109--130
Nathan Fieldsteel and
Hal Schenck Polynomial Interpolation in Higher
Dimension: From Simplicial Complexes to
GC Sets . . . . . . . . . . . . . . . . 131--143
David P. Nicholls Numerical Solution of Diffraction
Problems: a High-Order Perturbation of
Surfaces and Asymptotic Waveform
Evaluation Method . . . . . . . . . . . 144--167
Xiaojun Chen and
Lei Guo and
Zhaosong Lu and
Jane J. Ye An Augmented Lagrangian Method for
Non-Lipschitz Nonconvex Programming . . 168--193
Xiaobing Feng and
Yukun Li and
Yi Zhang Finite Element Methods for the
Stochastic Allen--Cahn Equation with
Gradient-type Multiplicative Noise . . . 194--216
Roger Temam and
Xiaoyan Wang Numerical Approximation of a Variational
Inequality Related to the Humid
Atmosphere . . . . . . . . . . . . . . . 217--239
Silvia Jerez and
Carlos Parés Entropy Stable Schemes for Degenerate
Convection--Diffusion Equations . . . . 240--264
Xiao Li and
Zhonghua Qiao and
Hui Zhang Convergence of a Fast Explicit Operator
Splitting Method for the Epitaxial
Growth Model with Slope Selection . . . 265--285
Max Gunzburger and
Nan Jiang and
Michael Schneier An Ensemble-Proper Orthogonal
Decomposition Method for the
Nonstationary Navier--Stokes Equations 286--304
Jialin Hong and
Xu Wang and
Liying Zhang Numerical Analysis on Ergodic Limit of
Approximations for Stochastic NLS
Equation via Multi-symplectic Scheme . . 305--327
Jingjun Zhao and
Yan Fan and
Yang Xu Stability of Symmetric Runge--Kutta
Methods for Neutral Delay
Integro-Differential Equations . . . . . 328--348
C. Carstensen and
K. Köhler Efficient Discrete Lagrange Multipliers
in three first-order finite element
discretizations for the \em A Posteriori
Error Control in an Obstacle Problem . . 349--375
Jörg Grande Analysis of Highly Accurate Finite
Element Based Algorithms for Computing
Distances to Level Sets . . . . . . . . 376--399
Zhiqiang Cai and
Cuiyu He and
Shun Zhang Discontinuous Finite Element Methods for
Interface Problems: Robust \em A Priori
and \em A Posteriori Error Estimates . . 400--418
Oliver Junge and
Daniel Matthes and
Horst Osberger A Fully Discrete Variational Scheme for
Solving Nonlinear Fokker--Planck
Equations in Multiple Space Dimensions 419--443
J. Frédéric Bonnans and
Adriano Festa Error Estimates for the Euler
Discretization of an Optimal Control
Problem with First-Order State
Constraints . . . . . . . . . . . . . . 445--471
Gabriel Acosta and
Juan Pablo Borthagaray A Fractional Laplace Equation:
Regularity of Solutions and Finite
Element Approximations . . . . . . . . . 472--495
Daniel Baffet and
Jan S. Hesthaven A Kernel Compression Scheme for
Fractional Differential Equations . . . 496--520
Buyang Li and
Weiwei Sun Maximal Regularity of Fully Discrete
Finite Element Solutions of Parabolic
Equations . . . . . . . . . . . . . . . 521--542
Eric T. Chung and
Weifeng Qiu Analysis of an SDG Method for the
Incompressible Navier--Stokes Equations 543--569
Zhilin Li and
Haifeng Ji and
Xiaohong Chen Accurate Solution and Gradient
Computation for Elliptic Interface
Problems with Variable Coefficients . . 570--597
Thorsten Hohage and
Frederic Weidling Characterizations of Variational Source
Conditions, Converse Results, and
Maxisets of Spectral Regularization
Methods . . . . . . . . . . . . . . . . 598--620
L. Banjai and
M. López-Fernández and
A. Schädle Fast and Oblivious Algorithms for
Dissipative and Two-dimensional Wave
Equations . . . . . . . . . . . . . . . 621--639
Weimin Han and
Mircea Sofonea and
Mikaël Barboteu Numerical Analysis of Elliptic
Hemivariational Inequalities . . . . . . 640--663
Giacomo Dimarco and
Lorenzo Pareschi Implicit--Explicit Linear Multistep
Methods for Stiff Kinetic Equations . . 664--690
Xiaobing Feng and
Max Jensen Convergent Semi-Lagrangian Methods for
the Monge--Amp\`ere Equation on
Unstructured Grids . . . . . . . . . . . 691--712
Armin Lechleiter and
Ruming Zhang A Convergent Numerical Scheme for
Scattering of Aperiodic Waves from
Periodic Surfaces Based on the
Floquet--Bloch Transform . . . . . . . . 713--736
Dietmar Gallistl Variational Formulation and Numerical
Analysis of Linear Elliptic Equations in
Nondivergence form with Cordes
Coefficients . . . . . . . . . . . . . . 737--757
Guoxian Chen and
Sebastian Noelle A New Hydrostatic Reconstruction Scheme
Based on Subcell Reconstructions . . . . 758--784
Marco Del Pra and
Alessio Fumagalli and
Anna Scotti Well Posedness of Fully Coupled
Fracture/Bulk Darcy Flow with XFEM . . . 785--811
André Schlichting and
Christian Seis Convergence Rates for Upwind Schemes
with Rough Coefficients . . . . . . . . 812--840
D. C. Antonopoulos and
V. A. Dougalis and
D. E. Mitsotakis Error Estimates for Galerkin
Approximations of the Serre Equations 841--868
Mohan K. Kadalbajoo and
Lok Pati Tripathi and
Alpesh Kumar An Error Analysis of a Finite Element
Method with IMEX-Time
Semidiscretizations for Some Partial
Integro-differential Inequalities
Arising in the Pricing of American
Options . . . . . . . . . . . . . . . . 869--891
Oscar P. Bruno and
Max Cubillos On the Quasi-unconditional Stability of
BDF--ADI Solvers for the Compressible
Navier--Stokes Equations and Related
Linear Problems . . . . . . . . . . . . 892--922
Patrick Henning and
Axel Målqvist The Finite Element Method for the
Time-Dependent Gross--Pitaevskii
Equation with Angular Momentum Rotation 923--952
Son L. Nguyen and
Tuan A. Hoang and
Dung T. Nguyen and
George Yin Milstein-Type Procedures for Numerical
Solutions of Stochastic Differential
Equations with Markovian Switching . . . 953--979
Makoto Mizuguchi and
Akitoshi Takayasu and
Takayuki Kubo and
Shin'ichi Oishi A Method of Verified Computations for
Solutions to Semilinear Parabolic
Equations Using Semigroup Theory . . . . 980--1001
H. Harbrecht and
M. D. Peters and
M. Schmidlin Uncertainty Quantification for PDEs with
Anisotropic Random Diffusion . . . . . . 1002--1023
Qinghai Zhang HFES: a Height Function Method with
Explicit Input and Signed Output for
High-Order Estimations of Curvature and
unit Vectors of Planar Curves . . . . . 1024--1056
Martin Stynes and
Eugene O'Riordan and
José Luis Gracia Error Analysis of a Finite Difference
Method on Graded Meshes for a
Time-Fractional Diffusion Equation . . . 1057--1079
John W. Barrett and
Klaus Deckelnick and
Vanessa Styles Numerical Analysis for a System Coupling
Curve Evolution to Reaction Diffusion on
the Curve . . . . . . . . . . . . . . . 1080--1100
Peter Benner and
Hamdullah Yücel Adaptive Symmetric Interior Penalty
Galerkin Method for Boundary Control
Problems . . . . . . . . . . . . . . . . 1101--1133
Hongxing Rui and
Xiaoli Li Stability and Superconvergence of MAC
Scheme for Stokes Equations on
Nonuniform Grids . . . . . . . . . . . . 1135--1158
Ana Alonso Rodríguez and
Enrico Bertolazzi and
Riccardo Ghiloni and
Ruben Specogna Efficient Construction of $2$-Chains
with a Prescribed Boundary . . . . . . . 1159--1187
Mario Ullrich A Monte Carlo Method for Integration of
Multivariate Smooth Functions . . . . . 1188--1200
Joel A. Rosenfeld and
Warren E. Dixon Approximating the Caputo Fractional
Derivative through the Mittag-Leffler
Reproducing Kernel Hilbert Space and the
Kernelized Adams--Bashforth--Moulton
Method . . . . . . . . . . . . . . . . . 1201--1217
Norbert Heuer and
Michael Karkulik A Robust DPG Method for Singularly
Perturbed Reaction-Diffusion Problems 1218--1242
Chao Zheng Weak Convergence Rate of a Time-Discrete
Scheme for the Heston Stochastic
Volatility Model . . . . . . . . . . . . 1243--1263
Claudia Schillings and
Andrew M. Stuart Analysis of the Ensemble Kalman Filter
for Inverse Problems . . . . . . . . . . 1264--1290
Philip L. Lederer and
Alexander Linke and
Christian Merdon and
Joachim Schöberl Divergence-free Reconstruction Operators
for Pressure-Robust Stokes
Discretizations with Continuous Pressure
Finite Elements . . . . . . . . . . . . 1291--1314
Robert Plato Converse Results, Saturation and
Quasi-optimality for Lavrentiev
Regularization of Accretive Problems . . 1315--1329
G. Ciaramella and
M. J. Gander Analysis of the Parallel Schwarz Method
for Growing Chains of Fixed-Sized
Subdomains: Part I . . . . . . . . . . . 1330--1356
Ricardo H. Nochetto and
Shawn W. Walker and
Wujun Zhang A Finite Element Method for Nematic
Liquid Crystals with Variable Degree of
Orientation . . . . . . . . . . . . . . 1357--1386
C. Besse and
G. Dujardin and
I. Lacroix-Violet High Order Exponential Integrators for
Nonlinear Schrödinger Equations with
Application to Rotating Bose--Einstein
Condensates . . . . . . . . . . . . . . 1387--1411
Arnd Rösch and
Gerd Wachsmuth Mass Lumping for the Optimal Control of
Elliptic Partial Differential Equations 1412--1436
Paolo Novati Some Properties of the Arnoldi-Based
Methods for Linear Ill-Posed Problems 1437--1455
Nicola Guglielmi and
Ivan Markovsky An ODE-Based Method for Computing the
Distance of Coprime Polynomials to
Common Divisibility . . . . . . . . . . 1456--1482
Volker Grimm and
Tanja Göckler Automatic Smoothness Detection of the
Resolvent Krylov Subspace Method for the
Approximation of $ C_0 $-Semigroups . . 1483--1504
Sören Bartels Numerical Solution of a Föppl-von Kármán
Model . . . . . . . . . . . . . . . . . 1505--1524
John C. Urschel On The Characterization and Uniqueness
of Centroidal Voronoi Tessellations . . 1525--1547
Ke Guo and
Deren Han and
Xiaoming Yuan Convergence Analysis of
Douglas--Rachford Splitting Method for
``Strongly + Weakly'' Convex Programming 1549--1577
Lucie Baudouin and
Maya de Buhan and
Sylvain Ervedoza Convergent Algorithm Based on Carleman
Estimates for the Recovery of a
Potential in the Wave Equation . . . . . 1578--1613
C. M. Mora and
H. A. Mardones and
J. C. Jimenez and
M. Selva and
R. Biscay A Stable Numerical Scheme for Stochastic
Differential Equations with
Multiplicative Noise . . . . . . . . . . 1614--1649
Bernardo Cockburn and
Guosheng Fu A Systematic Construction of Finite
Element Commuting Exact Sequences . . . 1650--1688
Mark Ainsworth and
Zhiping Mao Analysis and Approximation of a
Fractional Cahn--Hilliard Equation . . . 1689--1718
Wolfgang Bangerth and
Imbunm Kim and
Dongwoo Sheen and
Jaeryun Yim On Hanging Node Constraints for
Nonconforming Finite Elements using the
Douglas--Santos--Sheen--Ye Element as an
Example . . . . . . . . . . . . . . . . 1719--1739
L. Demkowicz and
J. Gopalakrishnan and
S. Nagaraj and
P. Sepúlveda A Spacetime DPG Method for the
Schrödinger Equation . . . . . . . . . . 1740--1759
Konstantin Brenner and
Clément Canc\`es Improving Newton's Method Performance by
Parametrization: The Case of the
Richards Equation . . . . . . . . . . . 1760--1785
Michael Feischl and
Thanh Tran The Eddy Current--LLG Equations:
FEM--BEM Coupling and A Priori Error
Estimates . . . . . . . . . . . . . . . 1786--1819
Laurent Bourgeois and
Jérémi Dardé The ``Exterior Approach'' Applied to the
Inverse Obstacle Problem for the Heat
Equation . . . . . . . . . . . . . . . . 1820--1842
Bastian Bohn and
Michael Griebel Error Estimates for Multivariate
Regression on Discretized Function
Spaces . . . . . . . . . . . . . . . . . 1843--1866
Christoph Reisinger and
Endre Süli and
Alan Whitley A Partial Fourier Transform Method for a
Class of Hypoelliptic Kolmogorov
Equations . . . . . . . . . . . . . . . 1867--1891
Pedro Ramaciotti and
Jean-Claude Nédélec About Some Boundary Integral Operators
on the Unit Disk Related to the Laplace
Equation . . . . . . . . . . . . . . . . 1892--1914
Son-Young Yi A Study of Two Modes of Locking in
Poroelasticity . . . . . . . . . . . . . 1915--1936
Thomas Apel and
Serge Nicaise and
Johannes Pfefferer Adapted Numerical Methods for the
Poisson Equation with $ L^2 $ Boundary
Data in NonConvex Domains . . . . . . . 1937--1957
Yanzhao Cao and
Jialin Hong and
Zhihui Liu Approximating Stochastic Evolution
Equations with Additive White and Rough
Noises . . . . . . . . . . . . . . . . . 1958--1981
Sander Rhebergen and
Garth N. Wells Analysis of a Hybridized/Interface
Stabilized Finite Element Method for the
Stokes Equations . . . . . . . . . . . . 1982--2003
Clemens Hofreither and
Stefan Takacs Robust Multigrid for Isogeometric
Analysis Based on Stable Splittings of
Spline Spaces . . . . . . . . . . . . . 2004--2024
Dmitriy Leykekhman and
Boris Vexler Global and Interior Pointwise best
Approximation Results for the Gradient
of Galerkin Solutions for Parabolic
Problems . . . . . . . . . . . . . . . . 2025--2049
Zhiming Chen and
Weiying Zheng PML Method for Electromagnetic
Scattering Problem in a Two-Layer Medium 2050--2084
Sebastiano Boscarino and
Lorenzo Pareschi and
Giovanni Russo A Unified IMEX Runge--Kutta Approach for
Hyperbolic Systems with Multiscale
Relaxation . . . . . . . . . . . . . . . 2085--2109
Do Y. Kwak and
Kye T. Wee and
Kwang S. Chang Erratum: An Analysis of a Broken $
P_1$-Nonconforming Finite Element Method
for Interface Problems . . . . . . . . . 2110--2111
Anthony P. Austin and
Lloyd N. Trefethen Trigonometric Interpolation and
Quadrature in Perturbed Points . . . . . 2113--2122
Selim Esedo\uglu and
Matt Jacobs Convolution Kernels and Stability of
Threshold Dynamics Methods . . . . . . . 2123--2150
Markus Bachmayr and
Albert Cohen and
Dinh D\uung and
Christoph Schwab Fully Discrete Approximation of
Parametric and Stochastic Elliptic PDEs 2151--2186
Federico Benvenuto A Study on Regularization for Discrete
Inverse Problems with Model-Dependent
Noise . . . . . . . . . . . . . . . . . 2187--2203
Antoine Levitt and
Christoph Ortner Convergence and Cycling in Walker-type
Saddle Search Algorithms . . . . . . . . 2204--2227
Eric Canc\`es and
Genevi\`eve Dusson and
Yvon Maday and
Benjamin Stamm and
Martin Vohralík Guaranteed and Robust a Posteriori
Bounds for Laplace Eigenvalues and
Eigenvectors: Conforming Approximations 2228--2254
Andy T. S. Wan and
Alexander Bihlo and
Jean-Christophe Nave Conservative Methods for Dynamical
Systems . . . . . . . . . . . . . . . . 2255--2285
Daniel Loghin Constraint Interface Preconditioning for
the Incompressible Stokes Equations . . 2286--2311
G. Manzini and
D. Funaro and
G. L. Delzanno Convergence of Spectral Discretizations
of the Vlasov--Poisson System . . . . . 2312--2335
Rodolfo R. Rosales and
Benjamin Seibold and
David Shirokoff and
Dong Zhou Unconditional Stability for Multistep
ImEx Schemes: Theory . . . . . . . . . . 2336--2360
Tao Yin and
George C. Hsiao and
Liwei Xu Boundary Integral Equation Methods for
the Two-Dimensional Fluid-Solid
Interaction Problem . . . . . . . . . . 2361--2393
Xingjie Helen Li and
Jianfeng Lu Quasi-nonlocal Coupling of Nonlocal
Diffusions . . . . . . . . . . . . . . . 2394--2415
Francis Filbet and
Luis Miguel Rodrigues Asymptotically Preserving
Particle-in-Cell Methods for
Inhomogeneous Strongly Magnetized
Plasmas . . . . . . . . . . . . . . . . 2416--2443
Irwin Yousept Hyperbolic Maxwell Variational
Inequalities for Bean's Critical-State
Model in Type-II Superconductivity . . . 2444--2464
Qiang Du and
Zhan Huang and
Philippe G. LeFloch Nonlocal Conservation Laws. A New Class
of Monotonicity-Preserving Models . . . 2465--2489
Fabian Müller and
Dominik Schötzau and
Christoph Schwab Symmetric Interior Penalty Discontinuous
Galerkin Methods for Elliptic Problems
in Polygons . . . . . . . . . . . . . . 2490--2521
Erik Burman and
Peter Hansbo and
Mats G. Larson The Penalty-Free Nitsche Method and
Nonconforming Finite Elements for the
Signorini Problem . . . . . . . . . . . 2523--2539
Charles Dossal and
Vincent Duval and
Clarice Poon Sampling the Fourier Transform Along
Radial Lines . . . . . . . . . . . . . . 2540--2564
Juan Vicente Gutiérrez-Santacreu and
Marco Restelli Inf-Sup Stable Finite Element Methods
for the Landau--Lifshitz--Gilbert and
Harmonic Map Heat Flow Equations . . . . 2565--2591
Lukas Drescher and
Holger Heumann and
Kersten Schmidt A High Order Method for the
Approximation of Integrals Over
Implicitly Defined Hypersurfaces . . . . 2592--2615
Gang Bao and
Chuchu Chen and
Peijun Li Inverse Random Source Scattering for
Elastic Waves . . . . . . . . . . . . . 2616--2643
C. Carstensen and
H. Rabus Axioms of Adaptivity with Separate
Marking for Data Resolution . . . . . . 2644--2665
Qingsong Zou and
Li Guo and
Quanling Deng High Order Continuous Local-Conserving
Fluxes and Finite-Volume-Like Finite
Element Solutions for Elliptic Equations 2666--2686
Michele Botti and
Daniele A. Di Pietro and
Pierre Sochala A Hybrid High-Order Method for Nonlinear
Elasticity . . . . . . . . . . . . . . . 2687--2717
Tom Gustafsson and
Rolf Stenberg and
Juha Videman Mixed and Stabilized Finite Element
Methods for the Obstacle Problem . . . . 2718--2744
Kristian Debrabant and
Giovanni Samaey and
Przemys\law Zieli\'nski A Micro-Macro Acceleration Method for
the Monte Carlo Simulation of Stochastic
Differential Equations . . . . . . . . . 2745--2786
Irwin Yousept and
Jun Zou Edge Element Method for Optimal Control
of Stationary Maxwell System with Gauss
Law . . . . . . . . . . . . . . . . . . 2787--2810
Alexandre Ern and
Iain Smears and
Martin Vohralík Guaranteed, Locally Space-Time
Efficient, and Polynomial-Degree Robust
a Posteriori Error Estimates for
High-Order Discretizations of Parabolic
Problems . . . . . . . . . . . . . . . . 2811--2834
Percy Deift and
Thomas Trogdon Universality for Eigenvalue Algorithms
on Sample Covariance Matrices . . . . . 2835--2862
Florian A. Potra A Superquadratic Variant of Newton's
Method . . . . . . . . . . . . . . . . . 2863--2884
Fatemeh Ghasemi and
Jan Nordström Coupling Requirements for Multiphysics
Problems Posed on Two Domains . . . . . 2885--2904
Long Chen and
Yongke Wu Convergence of Adaptive Mixed Finite
Element Methods for the Hodge Laplacian
Equation: Without Harmonic Forms . . . . 2905--2929
Zhaosong Lu and
Lin Xiao A Randomized Nonmonotone Block Proximal
Gradient Method for a Class of
Structured Nonlinear Programming . . . . 2930--2955
G. Manzini and
K. Lipnikov and
J. D. Moulton and
M. Shashkov Convergence Analysis of the mimetic
Finite Difference Method for Elliptic
Problems with Staggered Discretizations
of Diffusion Coefficients . . . . . . . 2956--2981
Bo Gong and
Wenbin Liu and
Tao Tang and
Weidong Zhao and
Tao Zhou An Efficient Gradient Projection Method
for Stochastic Optimal Control Problems 2982--3005
Jialin Hong and
Liying Sun and
Xu Wang High Order Conformal Symplectic and
Ergodic Schemes for the Stochastic
Langevin Equation via Generating
Functions . . . . . . . . . . . . . . . 3006--3029
Mario Chater and
Angxiu Ni and
Patrick J. Blonigan and
Qiqi Wang Least Squares Shadowing Method for
Sensitivity Analysis of Differential
Equations . . . . . . . . . . . . . . . 3030--3046
Tomás Chacón Rebollo and
Enrique Delgado Ávila and
Macarena Gómez Mármol and
Francesco Ballarin and
Gianluigi Rozza On a Certified Smagorinsky Reduced Basis
Turbulence Model . . . . . . . . . . . . 3047--3067
Ajay Jasra and
Kengo Kamatani and
Kody J. H. Law and
Yan Zhou Multilevel Particle Filters . . . . . . 3068--3096
Nicola Guglielmi and
Christian Lubich Matrix Stabilization Using Differential
Equations . . . . . . . . . . . . . . . 3097--3119
Jean-Luc Guermond and
Bojan Popov Invariant Domains and Second-Order
Continuous Finite Element Approximation
for Scalar Conservation Equations . . . 3120--3146
D. P. Kouri A Measure Approximation for
Distributionally Robust PDE-Constrained
Optimization Problems . . . . . . . . . 3147--3172
Yajing Li and
Yejuan Wang and
Weihua Deng Galerkin Finite Element Approximations
for Stochastic Space-Time Fractional
Wave Equations . . . . . . . . . . . . . 3173--3202
Pascal Azerad and
Jean-Luc Guermond and
Bojan Popov Well-Balanced Second-Order Approximation
of the Shallow Water Equation with
Continuous Finite Elements . . . . . . . 3203--3224
Bangti Jin and
Buyang Li and
Zhi Zhou Numerical Analysis of Nonlinear
Subdiffusion Equations . . . . . . . . . 1--23
Zhiping Mao and
George Em Karniadakis A Spectral Method (of Exponential
Convergence) for Singular Solutions of
the Diffusion Equation with General
Two-Sided Fractional Derivative . . . . 24--49
Emmanuel Gobet and
Gang Liu and
Jorge P. Zubelli A Nonintrusive Stratified Resampler for
Regression Monte Carlo: Application to
Solving Nonlinear Equations . . . . . . 50--77
Cecilia F. Mondaini and
Edriss S. Titi Uniform-in-Time Error Estimates for the
Postprocessing Galerkin Method Applied
to a Data Assimilation Algorithm . . . . 78--110
Robert N. Gantner and
Lukas Herrmann and
Christoph Schwab Quasi--Monte Carlo Integration for
Affine-Parametric, Elliptic PDEs: Local
Supports and Product Weights . . . . . . 111--135
Wei Yang and
Jichun Li and
Yunqing Huang Mathematical Analysis and Finite Element
Time Domain Simulation of Arbitrary
Star-Shaped Electromagnetic Cloaks . . . 136--159
Johannes Schwab and
Sergiy Pereverzyev, Jr. and
Markus Haltmeier A Galerkin Least Squares Approach for
Photoacoustic Tomography . . . . . . . . 160--184
Naveed Ahmed and
Alexander Linke and
Christian Merdon On Really Locking-Free Mixed Finite
Element Methods for the Transient
Incompressible Stokes Equations . . . . 185--209
Yubin Yan and
Monzorul Khan and
Neville J. Ford An Analysis of the Modified $ L_1 $
Scheme for Time-Fractional Partial
Differential Equations with Nonsmooth
Data . . . . . . . . . . . . . . . . . . 210--227
Jörg Grande and
Christoph Lehrenfeld and
Arnold Reusken Analysis of a High-Order Trace Finite
Element Method for PDEs on Level Set
Surfaces . . . . . . . . . . . . . . . . 228--255
Magnus Svärd and
Mark H. Carpenter and
Matteo Parsani Entropy Stability and the No-Slip Wall
Boundary Condition . . . . . . . . . . . 256--273
Davoud Mirzaei A Petrov--Galerkin Kernel Approximation
on the Sphere . . . . . . . . . . . . . 274--295
Jun Hu and
Guozhu Yu A Unified Analysis of Quasi-Optimal
Convergence for Adaptive Mixed Finite
Element Methods . . . . . . . . . . . . 296--316
Ernesto Cáceres and
Gabriel N. Gatica and
Filánder A. Sequeira A Mixed Virtual Element Method for
Quasi-Newtonian Stokes Flows . . . . . . 317--343
Wei Wang and
Xuejun Xu A Two-Level Overlapping Hybrid Domain
Decomposition Method for Eigenvalue
Problems . . . . . . . . . . . . . . . . 344--368
Chupeng Ma and
Liqun Cao A Crank--Nicolson Finite Element Method
and the Optimal Error Estimates for the
Modified Time-Dependent
Maxwell--Schrödinger Equations . . . . . 369--396
Max Gunzburger and
Xiaoming He and
Buyang Li On Stokes--Ritz Projection and Multistep
Backward Differentiation Schemes in
Decoupling the Stokes--Darcy Model . . . 397--427
P. Bringmann and
C. Carstensen and
G. Starke An Adaptive Least-Squares FEM for Linear
Elasticity with Optimal Convergence
Rates . . . . . . . . . . . . . . . . . 428--447
Mohammad Motamed and
Daniel Appelö A MultiOrder Discontinuous Galerkin
Monte Carlo Method for Hyperbolic
Problems with Stochastic Parameters . . 448--468
Augustin Chevallier and
Stefan Engblom Pathwise Error Bounds in Multiscale
Variable Splitting Methods for Spatial
Stochastic Kinetics . . . . . . . . . . 469--498
Karsten Kahl and
Nils Kintscher Geometric Multigrid for the
Tight-Binding Hamiltonian of Graphene 499--519
Yong Liu and
Chi-Wang Shu and
Mengping Zhang Optimal Error Estimates of the
Semidiscrete Central Discontinuous
Galerkin Methods for Linear Hyperbolic
Equations . . . . . . . . . . . . . . . 520--541
Konstantina Trivisa and
Franziska Weber Analysis and Simulations on a Model for
the Evolution of Tumors Under the
Influence of Nutrient and Drug
Application . . . . . . . . . . . . . . 542--569
Richard A. Norton and
Colin Fox and
Malcolm E. Morrison Numerical Approximation of the
Frobenius--Perron Operator using the
Finite Volume Method . . . . . . . . . . 570--589
Oyekola Oyekole and
Catalin Trenchea and
Martina Bukac A Second-Order in Time Approximation of
Fluid-Structure Interaction Problem . . 590--613
Ka Chun Cheung and
Leevan Ling and
Robert Schaback $ H^2 $-Convergence of Least-Squares
Kernel Collocation Methods . . . . . . . 614--633
Zhiming Chen and
Rui Tuo and
Wenlong Zhang Stochastic Convergence of a
Nonconforming Finite Element Method for
the Thin Plate Spline Smoother for
Observational Data . . . . . . . . . . . 635--659
Andre Laestadius and
Simen Kvaal Analysis of the Extended Coupled-Cluster
Method in Quantum Chemistry . . . . . . 660--683
Josef Dick and
Christian Irrgeher and
Gunther Leobacher and
Friedrich Pillichshammer On the Optimal Order of Integration in
Hermite Spaces with Finite Smoothness 684--707
Daisuke Furihata and
Mihály Kovács and
Stig Larsson and
Fredrik Lindgren Strong Convergence of a Fully Discrete
Finite Element Approximation of the
Stochastic Cahn--Hilliard Equation . . . 708--731
Waixiang Cao and
Chi-Wang Shu and
Yang Yang and
Zhimin Zhang Superconvergence of Discontinuous
Galerkin Method for Scalar Nonlinear
Hyperbolic Equations . . . . . . . . . . 732--765
Buyang Li and
Jiwei Zhang and
Chunxiong Zheng An Efficient Second-Order Finite
Difference Method for the
One-Dimensional Schrödinger Equation with
Absorbing Boundary Conditions . . . . . 766--791
Yu-Wen Li Global Superconvergence of the
Lowest-Order Mixed Finite Element on
Mildly Structured Meshes . . . . . . . . 792--815
J. A. Fiordilino A Second Order Ensemble Timestepping
Algorithm for Natural Convection . . . . 816--837
Georgios E. Zouraris Crank--Nicolson Finite Element
Approximations for a Linear Stochastic
Fourth Order Equation with Additive
Space-Time White Noise . . . . . . . . . 838--858
Yan Luo and
Zhu Wang An Ensemble Algorithm for Numerical
Solutions to Deterministic and Random
Parabolic PDEs . . . . . . . . . . . . . 859--876
Oliver G. Ernst and
Björn Sprungk and
Lorenzo Tamellini Convergence of Sparse Collocation for
Functions of Countably Many Gaussian
Random Variables (with Application to
Elliptic PDEs) . . . . . . . . . . . . . 877--905
Prashant K. Jha and
Robert Lipton Numerical Analysis of Nonlocal Fracture
Models in Hölder Space . . . . . . . . . 906--941
Jingwei Hu and
Ruiwen Shu and
Xiangxiong Zhang Asymptotic-Preserving and
Positivity-Preserving Implicit-Explicit
Schemes for the Stiff BGK Equation . . . 942--973
Michael Griebel and
Guanglian Li On the Decay Rate of the Singular Values
of Bivariate Functions . . . . . . . . . 974--993
Marcus J. Grote and
Michaela Mehlin and
Stefan A. Sauter Convergence Analysis of Energy
Conserving Explicit Local Time-Stepping
Methods for the Wave Equation . . . . . 994--1021
Nicolas Gillis and
Punit Sharma Finding the Nearest Positive-Real System 1022--1047
Viktor Linders and
Tomas Lundquist and
Jan Nordström On the order of Accuracy of Finite
Difference Operators on Diagonal Norm
Based Summation-by-Parts Form . . . . . 1048--1063
Yosra Hafiene and
Jalal Fadili and
Abderrahim Elmoataz Nonlocal $p$-Laplacian Evolution
Problems on Graphs . . . . . . . . . . . 1064--1090
Carsten Carstensen and
Friederike Hellwig Optimal Convergence Rates for Adaptive
Lowest-Order Discontinuous
Petrov--Galerkin Schemes . . . . . . . . 1091--1111
Hong-lin Liao and
Dongfang Li and
Jiwei Zhang Sharp Error Estimate of the Nonuniform
L1 Formula for Linear
Reaction-Subdiffusion Equations . . . . 1112--1133
Ankit Gupta and
Muruhan Rathinam and
Mustafa Khammash Estimation of Parameter Sensitivities
for Stochastic Reaction Networks Using
Tau-Leap Simulations . . . . . . . . . . 1134--1167
Chao Zeng and
Chunlin Wu On the Edge Recovery Property of
Noncovex Nonsmooth Regularization in
Image Restoration . . . . . . . . . . . 1168--1182
Pauline Lafitte and
Annelies Lejon and
Giovanni Samaey Erratum: A High-Order
Asymptotic-Preserving Scheme for Kinetic
Equations Using Projective Integration 1183--1185
Begoña Cano and
María Jesús Moreta Exponential Quadrature Rules Without
Order Reduction for Integrating Linear
Initial Boundary Value Problems . . . . 1187--1209
L. Beirão da Veiga and
C. Lovadina and
G. Vacca Virtual Elements for the Navier--Stokes
Problem on Polygonal Meshes . . . . . . 1210--1242
Nicole Cusimano and
Félix del Teso and
Luca Gerardo-Giorda and
Gianni Pagnini Discretizations of the Spectral
Fractional Laplacian on General Domains
with Dirichlet, Neumann, and Robin
Boundary Conditions . . . . . . . . . . 1243--1272
Christian Lubich and
Bart Vandereycken and
Hanna Walach Time Integration of Rank-Constrained
Tucker Tensors . . . . . . . . . . . . . 1273--1290
Chengda Wu and
Weiwei Sun Analysis of Galerkin FEMs for Mixed
Formulation of Time-Dependent
Ginzburg--Landau Equations Under
Temporal Gauge . . . . . . . . . . . . . 1291--1312
Xiaoli Li and
Hongxing Rui Superconvergence of Characteristics
Marker and Cell Scheme for the
Navier--Stokes Equations on Nonuniform
Grids . . . . . . . . . . . . . . . . . 1313--1337
Haijun Wu and
Jun Zou Finite Element Method and its Analysis
for a Nonlinear Helmholtz Equation with
High Wave Numbers . . . . . . . . . . . 1338--1359
Roel Matthysen and
Daan Huybrechs Function Approximation on Arbitrary
Domains Using Fourier Extension Frames 1360--1385
Qiang Du and
Xingjie Helen Li and
Jianfeng Lu and
Xiaochuan Tian A Quasi-nonlocal Coupling Method for
Nonlocal and Local Diffusion Models . . 1386--1404
Theodoros Katsaounis and
Irene Kyza A Posteriori Error Analysis for
Evolution Nonlinear Schrödinger Equations
up to the Critical Exponent . . . . . . 1405--1434
Xiaoyue Li and
Qianlin Ma and
Hongfu Yang and
Chenggui Yuan The Numerical Invariant Measure of
Stochastic Differential Equations With
Markovian Switching . . . . . . . . . . 1435--1455
Dimitri Breda and
Davide Liessi Approximation of Eigenvalues of
Evolution Operators for Linear Renewal
Equations . . . . . . . . . . . . . . . 1456--1481
Runchang Lin and
Xiu Ye and
Shangyou Zhang and
Peng Zhu A Weak Galerkin Finite Element Method
for Singularly Perturbed
Convection--Diffusion-Reaction Problems 1482--1497
G. Ciaramella and
M. J. Gander Analysis of the Parallel Schwarz Method
for Growing Chains of Fixed-sized
Subdomains: Part II . . . . . . . . . . 1498--1524
Erik Burman and
Alexandre Ern An Unfitted Hybrid High-Order Method for
Elliptic Interface Problems . . . . . . 1525--1546
Arieh Iserles and
Karolina Kropielnicka and
Pranav Singh Magnus--Lanczos Methods with Simplified
Commutators for the Schrödinger Equation
with a Time-Dependent Potential . . . . 1547--1569
Dietmar Gallistl and
Patrick Henning and
Barbara Verfürth Numerical Homogenization of $ H({\rm
curl}) $-Problems . . . . . . . . . . . 1570--1596
Xiaoliang Wan and
Haijun Yu and
Jiayu Zhai Convergence Analysis of a Finite Element
Approximation of Minimum Action Methods 1597--1620
Andreas Veeser and
Pietro Zanotti Quasi-Optimal Nonconforming Methods for
Symmetric Elliptic Problems. I ---
Abstract Theory . . . . . . . . . . . . 1621--1642
Christoph Lehrenfeld and
Maxim A. Olshanskii and
Xianmin Xu A Stabilized Trace Finite Element Method
for Partial Differential Equations on
Evolving Surfaces . . . . . . . . . . . 1643--1672
Samir Karaa Semidiscrete Finite Element Analysis of
Time Fractional Parabolic Problems: a
Unified Approach . . . . . . . . . . . . 1673--1692
Xuefeng Xu and
Chen-Song Zhang On the Ideal Interpolation Operator in
Algebraic Multigrid Methods . . . . . . 1693--1710
Fleurianne Bertrand First-Order System Least-Squares for
Interface Problems . . . . . . . . . . . 1711--1730
Christina C. Christara and
Nat Chun-Ho Leung Analysis of Quantization Error in
Financial Pricing via Finite Difference
Methods . . . . . . . . . . . . . . . . 1731--1757
Susanne C. Brenner and
Joscha Gedicke and
Li-yeng Sung $ C^0 $ Interior Penalty Methods for an
Elliptic Distributed Optimal Control
Problem on Nonconvex Polygonal Domains
with Pointwise State Constraints . . . . 1758--1785
W.-J. Beyn and
D. Otten and
J. Rottmann-Matthes Computation and Stability of Traveling
Waves in Second Order Evolution
Equations . . . . . . . . . . . . . . . 1786--1817
Todd Arbogast and
Chieh-Sen Huang and
Xikai Zhao Accuracy of WENO and Adaptive Order WENO
Reconstructions for Solving Conservation
Laws . . . . . . . . . . . . . . . . . . 1818--1847
Tomás Dohnal and
Ben Schweizer A Bloch Wave Numerical Scheme for
Scattering Problems in Periodic
Wave-Guides . . . . . . . . . . . . . . 1848--1870
I. G. Graham and
F. Y. Kuo and
D. Nuyens and
R. Scheichl and
I. H. Sloan Analysis of Circulant Embedding Methods
for Sampling Stationary Random Fields 1871--1895
Sören Bartels and
Lars Diening and
Ricardo H. Nochetto Unconditional Stability of Semi-Implicit
Discretizations of Singular Flows . . . 1896--1914
Wenbo Li and
Ricardo H. Nochetto Optimal Pointwise Error Estimates for
Two-Scale Methods for the
Monge--Amp\`ere Equation . . . . . . . . 1915--1941
Qi Sun and
Qiang Du and
Ju Ming Asymptotically Compatible Schemes for
Stochastic Homogenization . . . . . . . 1942--1960
Katharina Rafetseder and
Walter Zulehner A Decomposition Result for Kirchhoff
Plate Bending Problems and a New
Discretization Approach . . . . . . . . 1961--1986
Ralf Kornhuber and
Evgenia Youett Adaptive Multilevel Monte Carlo Methods
for Stochastic Variational Inequalities 1987--2007
Carsten Carstensen and
Johannes Storn Asymptotic Exactness of the
Least-Squares Finite Element Residual 2008--2028
Habib Ammari and
Matias Ruiz and
Sanghyeon Yu and
Hai Zhang Field expansions for Systems of Strongly
Coupled Plasmonic Nanoparticles . . . . 2029--2044
Jianbo Cui and
Jialin Hong Analysis of a Splitting Scheme for
Damped Stochastic Nonlinear Schrödinger
Equation with Multiplicative Noise . . . 2045--2069
Philip L. Lederer and
Christoph Lehrenfeld and
Joachim Schöberl Hybrid Discontinuous Galerkin Methods
with Relaxed H(div)-Conformity for
Incompressible Flows. Part I . . . . . . 2070--2094
Yongchao Liu and
Xiaoming Yuan and
Shangzhi Zeng and
Jin Zhang Partial Error Bound Conditions and the
Linear Convergence Rate of the
Alternating Direction Method of
Multipliers . . . . . . . . . . . . . . 2095--2123
Kailiang Wu Positivity-Preserving Analysis of
Numerical Schemes for Ideal
Magnetohydrodynamics . . . . . . . . . . 2124--2147
Elisabetta Carlini and
Francisco J. Silva On the Discretization of Some Nonlinear
Fokker--Planck--Kolmogorov Equations and
Applications . . . . . . . . . . . . . . 2148--2177
Dmitriy Leykekhman and
Boris Vexler Discrete Maximal Parabolic Regularity
for Galerkin Finite Element Methods for
Nonautonomous Parabolic Problems . . . . 2178--2202
Wietse M. Boon and
Jan M. Nordbotten and
Ivan Yotov Robust Discretization of Flow in
Fractured Porous Media . . . . . . . . . 2203--2233
Sarah Eckstein and
Michael Ruzicka On the Full Space-Time Discretization of
the Generalized Stokes Equations: The
Dirichlet Case . . . . . . . . . . . . . 2234--2261
Wei Gong and
Weiwei Hu and
Mariano Mateos and
John Singler and
Xiao Zhang and
Yangwen Zhang A New HDG Method for Dirichlet Boundary
Control of Convection Diffusion PDEs II:
Low Regularity . . . . . . . . . . . . . 2262--2287
Théophile Chaumont-Frelet and
Serge Nicaise and
David Pardo Finite Element Approximation of
Electromagnetic Fields Using Nonfitting
Meshes for Geophysics . . . . . . . . . 2288--2321
Zhongjian Wang and
Jack Xin and
Zhiwen Zhang Computing Effective Diffusivity of
Chaotic and Stochastic Flows Using
Structure-Preserving Schemes . . . . . . 2322--2344
Dominik Meidner and
Johannes Pfefferer and
Klemens Schürholz and
Boris Vexler $ h p$-Finite Elements for Fractional
Diffusion . . . . . . . . . . . . . . . 2345--2374
Yahya Alnashri and
Jérôme Droniou A Gradient Discretization Method to
Analyze Numerical Schemes for Nonlinear
Variational Inequalities, Application to
the Seepage Problem . . . . . . . . . . 2375--2405
Sven Gross and
Thomas Jankuhn and
Maxim A. Olshanskii and
Arnold Reusken A Trace Finite Element Method for
Vector-Laplacians on Surfaces . . . . . 2406--2429
Yan Li and
Zhengce Zhang and
Bei Hu Convergence Rate of an Explicit Finite
Difference Scheme for a Credit Rating
Migration Problem . . . . . . . . . . . 2430--2460
Rénald Chalayer and
Laurent Chupin and
Thierry Dubois A Bi-Projection Method for
Incompressible Bingham Flows with
Variable Density, Viscosity, and Yield
Stress . . . . . . . . . . . . . . . . . 2461--2483
Mustafa Aggul and
Jeffrey M. Connors and
Dilek Erkmen and
Alexander E. Labovsky A Defect-Deferred Correction Method for
Fluid-Fluid Interaction . . . . . . . . 2484--2512
Sergio Blanes Time-Average on the Numerical
Integration of Nonautonomous
Differential Equations . . . . . . . . . 2513--2536
Dirk Blömker and
Claudia Schillings and
Philipp Wacker A Strongly Convergent Numerical Scheme
from Ensemble Kalman Inversion . . . . . 2537--2562
Maxime Louis and
Benjamin Charlier and
Paul Jusselin and
Susovan Pal and
Stanley Durrleman A Fanning Scheme for the Parallel
Transport along Geodesics on Riemannian
Manifolds . . . . . . . . . . . . . . . 2563--2584
Claudine Leonhard and
Andreas Rößler Enhancing the Order of the Milstein
Scheme for Stochastic Partial
Differential Equations with Commutative
Noise . . . . . . . . . . . . . . . . . 2585--2622
Geir Bogfjellmo and
Klas Modin and
Olivier Verdier A Numerical Algorithm for $ C^2
$-Splines on Symmetric Spaces . . . . . 2623--2647
Carsten Carstensen and
Asha K. Dond and
Neela Nataraj and
Amiya K. Pani Three First-Order Finite Volume Element
Methods for Stokes Equations under
Minimal Regularity Assumptions . . . . . 2648--2671
Yabing Sun and
Weidong Zhao and
Tao Zhou Explicit theta-Schemes for Mean-Field
Backward Stochastic Differential
Equations . . . . . . . . . . . . . . . 2672--2697
Qi Sun and
Qiang Du and
Ju Ming Erratum: Asymptotically Compatible
Schemes for Stochastic Homogenization 2698--2699
Assyr Abdulle and
Timothée Pouchon Effective Models for Long Time Wave
Propagation in Locally Periodic Media 2701--2730
Pierre Cantin and
Norbert Heuer A DPG Framework for Strongly Monotone
Operators . . . . . . . . . . . . . . . 2731--2750
Andy T. S. Wan and
Jean-Christophe Nave On the Arbitrarily Long-Term Stability
of Conservative Methods . . . . . . . . 2751--2775
Mark S. Gockenbach and
Matthew J. Roberts Approximating the Generalized Singular
Value Expansion . . . . . . . . . . . . 2776--2795
Long Chen and
Xuehai Huang Decoupling of Mixed Methods Based on
Generalized Helmholtz Decompositions . . 2796--2825
Johnny Guzmán and
Michael Neilan Inf-Sup Stable Finite Elements on
Barycentric Refinements Producing
Divergence-Free Approximations in
Arbitrary Dimensions . . . . . . . . . . 2826--2844
Roberta Bianchini and
Laurent Gosse A Truly Two-Dimensional Discretization
of Drift-Diffusion Equations on
Cartesian Grids . . . . . . . . . . . . 2845--2870
Andreas Veeser and
Pietro Zanotti Quasi-Optimal Nonconforming Methods for
Symmetric Elliptic Problems. III ---
Discontinuous Galerkin and Other
Interior Penalty Methods . . . . . . . . 2871--2894
Jie Shen and
Jie Xu Convergence and Error Analysis for the
Scalar Auxiliary Variable (SAV) Schemes
to Gradient Flows . . . . . . . . . . . 2895--2912
Shuhao Cao and
Long Chen Anisotropic Error Estimates of the
Linear Virtual Element Method on
Polygonal Meshes . . . . . . . . . . . . 2913--2939
L. Beirão da Veiga and
F. Brezzi and
F. Dassi and
L. D. Marini and
A. Russo A Family of Three-Dimensional Virtual
Elements with Applications to
Magnetostatics . . . . . . . . . . . . . 2940--2962
Andrea Bonito and
Alan Demlow and
Justin Owen A Priori Error Estimates for Finite
Element Approximations to Eigenvalues
and Eigenfunctions of the
Laplace--Beltrami Operator . . . . . . . 2963--2988
U. S. Fjordholm and
K. Lye and
S. Mishra Numerical Approximation of Statistical
Solutions of Scalar Conservation Laws 2989--3009
Zhijiang Zhang and
Weihua Deng and
George Em Karniadakis A Riesz Basis Galerkin Method for the
Tempered Fractional Laplacian . . . . . 3010--3039
Chenglong Zhang and
Irene M. Gamba A Conservative Discontinuous Galerkin
Solver for the Space Homogeneous
Boltzmann Equation for Binary
Interactions . . . . . . . . . . . . . . 3040--3070
Manuel J. Castro Díaz and
Christophe Chalons and
Tomás Morales de Luna A Fully Well-Balanced
Lagrange-Projection-Type Scheme for the
Shallow-Water Equations . . . . . . . . 3071--3098
Michael Neilan and
Wujun Zhang Rates of Convergence in $ W^2_p $-Norm
for the Monge--Amp\`ere Equation . . . . 3099--3120
Diane Guignard and
Fabio Nobile A Posteriori Error Estimation for the
Stochastic Collocation Finite Element
Method . . . . . . . . . . . . . . . . . 3121--3143
Zhenning Cai and
Yanli Wang Suppression of Recurrence in the
Hermite-Spectral Method for Transport
Equations . . . . . . . . . . . . . . . 3144--3168
Denis Belomestny and
John Schoenmakers Projected Particle Methods for Solving
McKean--Vlasov Stochastic Differential
Equations . . . . . . . . . . . . . . . 3169--3195
J. Gopalakrishnan and
M. Neumüller and
P. S. Vassilevski The Auxiliary Space Preconditioner for
the de Rham Complex . . . . . . . . . . 3196--3218
Jisheng Kou and
Shuyu Sun and
Xiuhua Wang Linearly Decoupled Energy-Stable
Numerical Methods for Multicomponent
Two-Phase Compressible Flow . . . . . . 3219--3248
Weihua Deng and
Buyang Li and
Zhi Qian and
Hong Wang Time Discretization of a Tempered
Fractional Feynman--Kac Equation with
Measure Data . . . . . . . . . . . . . . 3249--3275
Leah Isherwood and
Zachary J. Grant and
Sigal Gottlieb Strong Stability Preserving Integrating
Factor Runge--Kutta Methods . . . . . . 3276--3307
Hao Li and
Shusen Xie and
Xiangxiong Zhang A High Order Accurate Bound-Preserving
Compact Finite Difference Scheme for
Scalar Convection Diffusion Equations 3308--3345
Peter Binev Tree Approximation for hp-Adaptivity . . 3346--3357
Qin Li and
Ruiwen Shu and
Li Wang A New Numerical Approach to Inverse
Transport Equation with Error Analysis 3358--3385
Peter Giesl and
Holger Wendland Kernel-Based Discretization for Solving
Matrix-Valued PDEs . . . . . . . . . . . 3386--3406
Bernardo Cockburn and
Guosheng Fu and
Weifeng Qiu Discrete $ H^1 $-Inequalities for Spaces
Admitting $M$-Decompositions . . . . . . 3407--3429
Andrei Cozma and
Christoph Reisinger Strong Convergence Rates for Euler
Approximations to a Class of Stochastic
Path-Dependent Volatility Models . . . . 3430--3458
Ivan V. Oseledets and
Maxim V. Rakhuba and
André Uschmajew Alternating Least Squares as Moving
Subspace Correction . . . . . . . . . . 3459--3479
Erik Burman and
Mats G. Larson and
Lauri Oksanen Primal-Dual Mixed Finite Element Methods
for the Elliptic Cauchy Problem . . . . 3480--3509
Herbert Egger and
Christoph Erath and
Robert Schorr On the Nonsymmetric Coupling Method for
Parabolic--Elliptic Interface Problems 3510--3533
Ricardo J. Alonso and
Irene M. Gamba and
Sri Harsha Tharkabhushanam Convergence and Error Estimates for the
Lagrangian-Based Conservative Spectral
Method for Boltzmann Equations . . . . . 3534--3579
Giovanni Russo and
Seok-Bae Yun Convergence of a Semi-Lagrangian Scheme
for the Ellipsoidal BGK Model of the
Boltzmann Equation . . . . . . . . . . . 3580--3610
Félix del Teso and
Jòrgen Endal and
Espen R. Jakobsen Robust Numerical Methods for Nonlocal
(and Local) Equations of Porous Medium
Type. Part II: Schemes and Experiments 3611--3647
Susanne Solem Convergence Rates of the Front Tracking
Method for Conservation Laws in the
Wasserstein Distances . . . . . . . . . 3648--3666
Alberto Paganini and
Kevin Sturm Weakly Normal Basis Vector Fields in
RKHS with an Application to Shape Newton
Methods . . . . . . . . . . . . . . . . 1--26
Fatemeh Mohammadi and
Carmen Arévalo and
Claus Führer A Polynomial Formulation of Adaptive
Strong Stability Preserving Multistep
Methods . . . . . . . . . . . . . . . . 27--43
Josef Dick and
Takashi Goda and
Takehito Yoshiki Richardson Extrapolation of Polynomial
Lattice Rules . . . . . . . . . . . . . 44--69
Chuchu Chen and
Di Liu Ergodic Approximation to Chemical
Reaction System with Delay . . . . . . . 70--95
Yonglin Li and
Haijun Wu FEM and CIP--FEM for Helmholtz Equation
with High Wave Number and Perfectly
Matched Layer Truncation . . . . . . . . 96--126
Hwi Lee and
Qiang Du Asymptotically Compatible SPH-Like
Particle Discretizations of One
Dimensional Linear Advection Models . . 127--147
Martin Campos-Pinto and
Frédérique Charles and
Bruno Després Algorithms For Positive Polynomial
Approximation . . . . . . . . . . . . . 148--172
Haodi Chen and
Genggeng Huang and
Xu-Jia Wang Convergence Rate Estimates for
Aleksandrov's Solution to the
Monge--Amp\`ere Equation . . . . . . . . 173--191
Ting Wang and
Petr Plechác Steady-State Sensitivity Analysis of
Continuous Time Markov Chains . . . . . 192--217
Hong-lin Liao and
William McLean and
Jiwei Zhang A Discrete Grönwall Inequality with
Applications to Numerical Schemes for
Subdiffusion Problems . . . . . . . . . 218--237
Yu Du and
Lu Zhang and
Zhimin Zhang Convergence Analysis of a Discontinuous
Galerkin Method for Wave Equations in
Second-Order Form . . . . . . . . . . . 238--265
Andreas Veeser and
Pietro Zanotti Quasi-Optimal Nonconforming Methods for
Symmetric Elliptic Problems. II ---
Overconsistency and Classical
Nonconforming Elements . . . . . . . . . 266--292
Lars Schmutz and
Thomas P. Wihler The Variable-Order Discontinuous
Galerkin Time Stepping Scheme for
Parabolic Evolution Problems is
Uniformly $ L^\infty $-Stable . . . . . 293--319
Huoyuan Duan and
Zhijie Du and
Wei Liu and
Shangyou Zhang New Mixed Elements for Maxwell Equations 320--354
Mark Ainsworth and
Shuai Jiang Preconditioning the Mass Matrix for High
Order Finite Element Approximation on
Triangles . . . . . . . . . . . . . . . 355--377
Andreas Neuenkirch and
Michaela Szölgyenyi and
Lukasz Szpruch An Adaptive Euler--Maruyama Scheme for
Stochastic Differential Equations with
Discontinuous Drift and its Convergence
Analysis . . . . . . . . . . . . . . . . 378--403
Philipp Grohs and
Hanne Hardering and
Oliver Sander and
Markus Sprecher Projection-Based Finite Elements for
Nonlinear Function Spaces . . . . . . . 404--428
Simon Baumstark and
Katharina Schratz Uniformly Accurate Oscillatory
Integrators for the
Klein--Gordon--Zakharov System from Low-
to High-Plasma Frequency Regimes . . . . 429--457
Feng Bao and
Lin Mu and
Jin Wang A Fully Computable A Posteriori Error
Estimate for the Stokes Equations on
Polytopal Meshes . . . . . . . . . . . . 458--477
Daniele Boffi and
Lucia Gastaldi Adaptive Finite Element Method for the
Maxwell Eigenvalue Problem . . . . . . . 478--494
Wenbin Chen and
Xiaoming Wang and
Yue Yan and
Zhuying Zhang A Second Order BDF Numerical Scheme with
Variable Steps for the Cahn--Hilliard
Equation . . . . . . . . . . . . . . . . 495--525
Thomas J. Murphy and
Noel J. Walkington Control Volume Approximation of
Degenerate Two-Phase Porous Flows . . . 527--546
Art Owen Effective Dimension of Some Weighted
Pre-Sobolev Spaces with Dominating Mixed
Partial Derivatives . . . . . . . . . . 547--562
Toshihiro Yamada An Arbitrary High Order Weak
Approximation of SDE and Malliavin Monte
Carlo: Analysis of Probability
Distribution Functions . . . . . . . . . 563--591
Dietmar Gallistl and
Endre Süli Mixed Finite Element Approximation of
the Hamilton--Jacobi--Bellman Equation
with Cordes Coefficients . . . . . . . . 592--614
Sara Pollock and
Leo G. Rebholz and
Mengying Xiao Anderson-Accelerated Convergence of
Picard Iterations for Incompressible
Navier--Stokes Equations . . . . . . . . 615--637
Lukasz P\lociniczak Numerical Method for the Time-Fractional
Porous Medium Equation . . . . . . . . . 638--656
Weizhu Bao and
Rémi Carles and
Chunmei Su and
Qinglin Tang Error Estimates of a Regularized Finite
Difference Method for the Logarithmic
Schrödinger Equation . . . . . . . . . . 657--680
Ka\"\is Ammari and
Carlos Castro Numerical Approximation of the Best
Decay Rate for Some Dissipative Systems 681--701
Chuchu Chen and
Jialin Hong and
Lihai Ji Runge--Kutta Semidiscretizations for
Stochastic Maxwell Equations with
Additive Noise . . . . . . . . . . . . . 702--727
Chuchu Chen and
Jialin Hong and
Lihai Ji Mean-Square Convergence of a
Semidiscrete Scheme for Stochastic
Maxwell Equations . . . . . . . . . . . 728--750
Ellya L. Kawecki A Discontinuous Galerkin Finite Element
Method for Uniformly Elliptic Two
Dimensional Oblique Boundary-Value
Problems . . . . . . . . . . . . . . . . 751--778
Binjie Li and
Hao Luo and
Xiaoping Xie Analysis of a Time-Stepping Scheme for
Time Fractional Diffusion Problems with
Nonsmooth Data . . . . . . . . . . . . . 779--798
Imran H. Biswas and
Indranil Chowdhury and
Espen R. Jakobsen On the Rate of Convergence for Monotone
Numerical Schemes for Nonlocal Isaacs
Equations . . . . . . . . . . . . . . . 799--827
Konstantinos Chrysafinos and
Efthymios N. Karatzas and
Dimitrios Kostas Stability and Error Estimates of Fully
Discrete Schemes for the Brusselator
System . . . . . . . . . . . . . . . . . 828--853
Zhijian He On the Error Rate of Conditional
Quasi--Monte Carlo for Discontinuous
Functions . . . . . . . . . . . . . . . 854--874
Qiang Du and
Lili Ju and
Xiao Li and
Zhonghua Qiao Maximum Principle Preserving Exponential
Time Differencing Schemes for the
Nonlocal Allen--Cahn Equation . . . . . 875--898
Marc Aur\`ele Gilles and
Alex Townsend Continuous Analogues of Krylov Subspace
Methods for Differential Operators . . . 899--924
Ph. Chartier and
M. Lemou and
F. Méhats and
G. Vilmart Highly Oscillatory Problems with
Time-Dependent Vanishing Frequency . . . 925--944
Brittany Froese Hamfeldt Convergence Framework for the Second
Boundary Value Problem for the
Monge--Amp\`ere Equation . . . . . . . . 945--971
Andrea Bonito and
Alan Demlow A Posteriori Error Estimates for the
Laplace--Beltrami Operator on Parametric
$ C^2 $ Surfaces . . . . . . . . . . . . 973--996
Xue-lei Lin and
Michael K. Ng and
Hai-Wei Sun Crank--Nicolson Alternative Direction
Implicit Method for Space-Fractional
Diffusion Equations with Nonseparable
Coefficients . . . . . . . . . . . . . . 997--1019
Lise-Marie Imbert-Gerard and
Felipe Vico and
Leslie Greengard and
Miguel Ferrando Integral Equation Methods for
Electrostatics, Acoustics, and
Electromagnetics in Smoothly Varying,
Anisotropic Media . . . . . . . . . . . 1020--1035
Johannes Eilinghoff and
Tobias Jahnke and
Roland Schnaubelt Error Analysis of an Energy Preserving
ADI Splitting Scheme for the Maxwell
Equations . . . . . . . . . . . . . . . 1036--1057
Shuhao Cao and
Long Chen Anisotropic Error Estimates of the
Linear Nonconforming Virtual Element
Methods . . . . . . . . . . . . . . . . 1058--1081
Rüdiger Verfürth and
Pietro Zanotti A Quasi-optimal Crouzeix--Raviart
Discretization of the Stokes Equations 1082--1099
Matt Jacobs and
Flavien Léger and
Wuchen Li and
Stanley Osher Solving Large-Scale Optimization
Problems with a Convergence Rate
Independent of Grid Size . . . . . . . . 1100--1123
Michael Feischl Optimality of a Standard Adaptive Finite
Element Method for the Stokes Problem 1124--1157
Zheng Sun and
Chi-wang Shu Strong Stability of Explicit
Runge--Kutta Time Discretizations . . . 1158--1182
Saad Qadeer and
Jon A. Wilkening Computing the Dirichlet--Neumann
Operator on a Cylinder . . . . . . . . . 1183--1204
Sergio Amat and
Juan Ruiz and
Chi-wang Shu On New Strategies to Control the
Accuracy of WENO Algorithms Close to
Discontinuities . . . . . . . . . . . . 1205--1237
Yujie Liu and
Junping Wang and
Qingsong Zou A Conservative Flux Optimization Finite
Element Method for Convection--diffusion
Equations . . . . . . . . . . . . . . . 1238--1262
Pierson T. Guthrey and
James A. Rossmanith The Regionally Implicit Discontinuous
Galerkin Method: Improving the Stability
of DG-FEM . . . . . . . . . . . . . . . 1263--1288
Wansheng Wang and
Yingzi Chen and
Hua Fang On the Variable Two-Step IMEX BDF Method
for Parabolic Integro-differential
Equations with Nonsmooth Initial Data
Arising in Finance . . . . . . . . . . . 1289--1317
Raimund Bürger and
Paul E. Méndez and
Ricardo Ruiz-Baier On $ H(d i v) $-conforming Methods for
Double-diffusion Equations in Porous
Media . . . . . . . . . . . . . . . . . 1318--1343
Vahid Keshavarzzadeh and
Robert M. Kirby and
Akil Narayan Convergence Acceleration for
Time-Dependent Parametric Multifidelity
Models . . . . . . . . . . . . . . . . . 1344--1368
Tomás Gergelits and
Kent-André Mardal and
Bjòrn Fredrik Nielsen and
Zdenek Strakos Laplacian Preconditioning of Elliptic
PDEs: Localization of the Eigenvalues of
the Discretized Operator . . . . . . . . 1369--1394
Chun'guang You and
Hehu Xie and
Xuefeng Liu Guaranteed Eigenvalue Bounds for the
Steklov Eigenvalue Problem . . . . . . . 1395--1410
Andreas Langer and
Fernando Gaspoz Overlapping Domain Decomposition Methods
for Total Variation Denoising . . . . . 1411--1444
Dongling Wang and
Jun Zou Dissipativity and Contractivity Analysis
for Fractional Functional Differential
Equations and their Numerical
Approximations . . . . . . . . . . . . . 1445--1470
Stephen Edward Moore Space--Time Multipatch Discontinuous
Galerkin Isogeometric Analysis for
Parabolic Evolution Problems . . . . . . 1471--1493
Ana Maria Soane and
Andrei Draganescu Multigrid Preconditioners for the
Newton--Krylov Method in the Optimal
Control of the Stationary Navier--Stokes
Equations . . . . . . . . . . . . . . . 1494--1523
Mariam Al-Maskari and
Samir Karaa Numerical Approximation of Semilinear
Subdiffusion Equations with Nonsmooth
Initial Data . . . . . . . . . . . . . . 1524--1544
Ruchi Guo and
Tao Lin A Higher Degree Immersed Finite Element
Method Based on a Cauchy Extension for
Elliptic Interface Problems . . . . . . 1545--1573
Yuan Xu and
Qiang Zhang and
Chi-wang Shu and
Haijin Wang The $ L^2 $-norm Stability Analysis of
Runge--Kutta Discontinuous Galerkin
Methods for Linear Hyperbolic Equations 1574--1601
Yongyong Cai and
Yan Wang Uniformly Accurate Nested Picard
Iterative Integrators for the Dirac
Equation in the Nonrelativistic Limit
Regime . . . . . . . . . . . . . . . . . 1602--1624
Christoph Reisinger and
Yufei Zhang A Penalty Scheme for Monotone Systems
with Interconnected Obstacles:
Convergence and Error Estimates . . . . 1625--1648
Brendan Keith and
Ali Vaziri Astaneh and
Leszek F. Demkowicz Goal-Oriented Adaptive Mesh Refinement
for Discontinuous Petrov--Galerkin
Methods . . . . . . . . . . . . . . . . 1649--1676
K. L. A. Kirk and
T. L. Horvath and
A. Cesmelioglu and
S. Rhebergen Analysis of a Space--Time Hybridizable
Discontinuous Galerkin Method for the
Advection--Diffusion Problem on
Time-Dependent Domains . . . . . . . . . 1677--1696
Jeonghun J. Lee and
Stephen J. Shannon and
Tan Bui-Thanh and
John N. Shadid Analysis of an HDG Method for Linearized
Incompressible Resistive MHD Equations 1697--1722
Juan Pablo Borthagaray and
Patrick Ciarlet Jr On the Convergence in $ H^1 $-Norm for
the Fractional Laplacian . . . . . . . . 1723--1743
Josef Dick and
Michael Feischl and
Christoph Schwab Improved Efficiency of a Multi-Index FEM
for Computational Uncertainty
Quantification . . . . . . . . . . . . . 1744--1769
Shixin Xu and
Xinfu Chen and
Chun Liu and
Xingye Yue Numerical Method for Multi-Alleles
Genetic Drift Problem . . . . . . . . . 1770--1788
Antti Hannukainen and
Jarmo Malinen and
Antti Ojalammi Efficient Solution of Symmetric
Eigenvalue Problems from Families of
Coupled Systems . . . . . . . . . . . . 1789--1814
Jianbo Cui and
Jialin Hong Strong and Weak Convergence Rates of a
Spatial Approximation for Stochastic
Partial Differential Equation with
One-sided Lipschitz Coefficient . . . . 1815--1841
José Antonio Carrillo and
Piotr Gwiazda and
Karolina Kropielnicka and
Anna K. Marciniak-Czochra The Escalator Boxcar Train Method for a
System of Age-Structured Equations in
the Space of Measures . . . . . . . . . 1842--1874
Hui Liang and
Hermann Brunner The Convergence of Collocation Solutions
in Continuous Piecewise Polynomial
Spaces for Weakly Singular Volterra
Integral Equations . . . . . . . . . . . 1875--1896
Vanja Nikoli\'c and
Barbara Wohlmuth A Priori Error Estimates for the Finite
Element Approximation of Westervelt's
Quasi-linear Acoustic Wave Equation . . 1897--1918
Gang Chen and
John R. Singler and
Yangwen Zhang An HDG Method for Dirichlet Boundary
Control of Convection Dominated
Diffusion PDEs . . . . . . . . . . . . . 1919--1946
Alexander Ostermann and
Chiara Piazzola and
Hanna Walach Convergence of a Low-Rank Lie--Trotter
Splitting for Stiff Matrix Differential
Equations . . . . . . . . . . . . . . . 1947--1966
Marvin Knöller and
Alexander Ostermann and
Katharina Schratz A Fourier Integrator for the Cubic
Nonlinear Schrödinger Equation with Rough
Initial Data . . . . . . . . . . . . . . 1967--1986
John W. Barrett and
Harald Garcke and
Robert Nürnberg Stable Discretizations of Elastic Flow
in Riemannian Manifolds . . . . . . . . 1987--2018
Yuwen Li Some Convergence and Optimality Results
of Adaptive Mixed Methods in Finite
Element Exterior Calculus . . . . . . . 2019--2042
Johannes Pfefferer and
Max Winkler Finite Element Error Estimates for
Normal Derivatives on Boundary
Concentrated Meshes . . . . . . . . . . 2043--2073
Abinand Gopal and
Lloyd N. Trefethen Solving Laplace Problems with Corner
Singularities via Rational Functions . . 2074--2094
Lei Li and
Jian-Guo Liu A Discretization of Caputo Derivatives
with Application to Time Fractional SDEs
and Gradient Flows . . . . . . . . . . . 2095--2120
Christian Poetzsche Numerical Dynamics of Integrodifference
Equations: Global Attractivity in a $
C^0 $-Setting . . . . . . . . . . . . . 2121--2141
Qi Tao and
Yan Xu Superconvergence of Arbitrary
Lagrangian--Eulerian Discontinuous
Galerkin Methods for Linear Hyperbolic
Equations . . . . . . . . . . . . . . . 2142--2165
Herbert Egger and
Matthias Schlottbom A Perfectly Matched Layer Approach for $
P_N $-Approximations in Radiative
Transfer . . . . . . . . . . . . . . . . 2166--2188
Jun Hu and
Shangyou Zhang and
Zhimin Zhang On the $ 2 p $ th-Order of Convergence
of the Galerkin Difference Method . . . 2189--2199
J. A. C. Weideman Gauss--Hermite Quadrature for the
Bromwich Integral . . . . . . . . . . . 2200--2216
Giovanni Migliorati Adaptive Approximation by Optimal
Weighted Least-Squares Methods . . . . . 2217--2245
Li Guo and
Hengguang Li and
Qingsong Zou Interior Estimates of Finite Volume
Element Methods Over Quadrilateral
Meshes for Elliptic Equations . . . . . 2246--2265
Felix del Teso and
Jòrgen Endal and
Espen R. Jakobsen Robust Numerical Methods for Nonlocal
(and Local) Equations of Porous Medium
Type. Part I: Theory . . . . . . . . . . 2266--2299
Adrian Sandu A Class of Multirate Infinitesimal GARK
Methods . . . . . . . . . . . . . . . . 2300--2327
I. Cravero and
M. Semplice and
G. Visconti Optimal Definition of the Nonlinear
Weights in Multidimensional Central
WENOZ Reconstructions . . . . . . . . . 2328--2358
Alex Bespalov and
Dirk Praetorius and
Leonardo Rocchi and
Michele Ruggeri Convergence of Adaptive Stochastic
Galerkin FEM . . . . . . . . . . . . . . 2359--2382
Lihui Chai and
Emmanuel Lorin and
Xu Yang Frozen Gaussian Approximation for the
Dirac Equation in Semiclassical Regime 2383--2412
Heiko Kröner Analysis of Constants in Error Estimates
for the Finite Element Approximation of
Regularized Nonlinear Geometric
Evolution Equations . . . . . . . . . . 2413--2435
J. Albella and
H. Ben Dhia and
S. Imperiale and
J. Rodríguez Mathematical and Numerical Study of
Transient Wave Scattering by Obstacles
with a New Class of Arlequin Coupling 2436--2468
Lu Zhang and
Thomas Hagstrom and
Daniel Appelö An Energy-Based Discontinuous Galerkin
Method for the Wave Equation with
Advection . . . . . . . . . . . . . . . 2469--2492
Gabriel N. Gatica and
Salim Meddahi On the Coupling of VEM and BEM in Two
and Three Dimensions . . . . . . . . . . 2493--2518
Hehu Xie and
Lei Zhang and
Houman Owhadi Fast Eigenpairs Computation with
Operator Adapted Wavelets and
Hierarchical Subspace Correction . . . . 2519--2550
Gang Chen and
Liangya Pi and
Liwei Xu and
Yangwen Zhang A Superconvergent Ensemble HDG Method
for Parameterized Convection Diffusion
Equations . . . . . . . . . . . . . . . 2551--2578
Fabian M. Faulstich and
Andre Laestadius and
Örs Legeza and
Reinhold Schneider and
Simen Kvaal Analysis of the Tailored Coupled-Cluster
Method in Quantum Chemistry . . . . . . 2579--2607
Jean-Marie Mirebeau Riemannian Fast-Marching on Cartesian
Grids, Using Voronoi's First Reduction
of Quadratic Forms . . . . . . . . . . . 2608--2655
Yongcun Song and
Xiaoming Yuan and
Hangrui Yue An Inexact Uzawa Algorithmic Framework
for Nonlinear Saddle Point Problems with
Applications to Elliptic Optimal Control
Problem . . . . . . . . . . . . . . . . 2656--2684
M. Winckler and
I. Yousept Fully Discrete Scheme for Bean's
Critical-state Model with Temperature
Effects in Superconductivity . . . . . . 2685--2706
Daan Huybrechs and
Arno Kuijlaars and
Nele Lejon A Numerical Method for Oscillatory
Integrals with Coalescing Saddle Points 2707--2729
Jikun Zhao and
Bei Zhang and
Shipeng Mao and
Shaochun Chen The Divergence-Free Nonconforming
Virtual Element for the Stokes Problem 2730--2759
Antonio Baeza and
Raimund Bürger and
Pep Mulet and
David Zorío WENO Reconstructions of Unconditionally
Optimal High Order . . . . . . . . . . . 2760--2784
Erik Burman and
Cuiyu He Primal Dual Mixed Finite Element Methods
for Indefinite Advection-Diffusion
Equations . . . . . . . . . . . . . . . 2785--2811
Jeremie Houssineau and
Ajay Jasra and
Sumeetpal S. Singh On Large Lag Smoothing for Hidden Markov
Models . . . . . . . . . . . . . . . . . 2812--2828
Hongyi Zhu and
Chuanju Xu A Fast High Order Method for the
Time-Fractional Diffusion Equation . . . 2829--2849
David I. Ketcheson Relaxation Runge--Kutta Methods:
Conservation and Stability for
Inner-Product Norms . . . . . . . . . . 2850--2870
D. C. Antonopoulos and
V. A. Dougalis and
D. E. Mitsotakis Corrigendum: Error Estimates for
Galerkin Approximations of the Serre
Equations . . . . . . . . . . . . . . . 3098--3101
Lexing Ying Sparse Fourier Transform via Butterfly
Algorithm . . . . . . . . . . . . . . . 1678--1694