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Hao Lu Stair Matrices and Their Generalizations
with Applications to Iterative Methods
I: A Generalization of the Successive
Overrelaxation Method . . . . . . . . . 1--17
Gabriel Acosta and
Ricardo G. Durán The Maximum Angle Condition for Mixed
and Nonconforming Elements: Application
to the Stokes Equations . . . . . . . . 18--36
John C. Strikwerda and
Young S. Lee The Accuracy of the Fractional Step
Method . . . . . . . . . . . . . . . . . 37--47
Dietrich Braess and
Wolfgang Dahmen and
Christian Wieners A Multigrid Algorithm for the Mortar
Finite Element Method . . . . . . . . . 48--69
B. Lee First-Order System Least-Squares for
Elliptic Problems with Robin Boundary
Conditions . . . . . . . . . . . . . . . 70--104
Bengt Fornberg and
Michelle Ghrist Spatial Finite Difference Approximations
for Wave-Type Equations . . . . . . . . 105--130
Hsing-Hsia Chen and
John C. Strikwerda Preconditioning for Regular Elliptic
Systems . . . . . . . . . . . . . . . . 131--151
Donghui Li and
Masao Fukushima A Globally and Superlinearly Convergent
Gauss--Newton-Based BFGS Method for
Symmetric Nonlinear Equations . . . . . 152--172
H. S. Tang and
T. Zhou On Nonconservative Algorithms for Grid
Interfaces . . . . . . . . . . . . . . . 173--193
Desmond J. Higham Trust Region Algorithms and Timestep
Selection . . . . . . . . . . . . . . . 194--210
René Pinnau and
Andreas Unterreiter The Stationary Current-Voltage
Characteristics of the Quantum
Drift-Diffusion Model . . . . . . . . . 211--245
Matthias K. Gobbert and
Andreas Prohl A Discontinuous Finite Element Method
for Solving a MultiWell Problem . . . . 246--268
Arne Marthinsen Interpolation in Lie Groups . . . . . . 269--285
John W. Barrett and
James F. Blowey and
Harald Garcke Finite Element Approximation of the
Cahn--Hilliard Equation with Degenerate
Mobility . . . . . . . . . . . . . . . . 286--318
Wolfgang Dahmen and
Rob Stevenson Element-by-Element Construction of
Wavelets Satisfying Stability and Moment
Conditions . . . . . . . . . . . . . . . 319--352
Luca F. Pavarino and
Olof B. Widlund Iterative Substructuring Methods for
Spectral Element Discretizations of
Elliptic Systems I: Compressible Linear
Elasticity . . . . . . . . . . . . . . . 353--374
Luca F. Pavarino and
Olof B. Widlund Iterative Substructuring Methods for
Spectral Element Discretizations of
Elliptic Systems. II: Mixed Methods for
Linear Elasticity and Stokes Flow . . . 375--402
Vladimir Druskin and
Leonid Knizhnerman Gaussian Spectral Rules for the
Three-Point Second Differences: I. A
Two-Point Positive Definite Problem in a
Semi-Infinite Domain . . . . . . . . . . 403--422
Clint Dawson and
Robert Kirby Solution of Parabolic Equations by
Backward Euler-Mixed Finite Element
Methods on a Dynamically Changing Mesh 423--442
Christoph Pflaum Robust Convergence of Multilevel
Algorithms for Convection-Diffusion
Equations . . . . . . . . . . . . . . . 443--469
Bosco García-Archilla and
Edriss S. Titi Postprocessing the Galerkin Method: The
Finite-Element Case . . . . . . . . . . 470--499
TaKeo K. Ushijima and
Shigetoshi Yazaki Convergence of a Crystalline Algorithm
for the Motion of a Closed Convex Curve
by a Power of Curvature \boldmath $ V =
K^A $ . . . . . . . . . . . . . . . . . 500--522
L. Zhornitskaya and
A. L. Bertozzi Positivity-Preserving Numerical Schemes
for Lubrication-Type Equations . . . . . 523--555
Thomas A. Manteuffel and
Klaus J. Ressel and
Gerhard Starke A Boundary Functional for the
Least-Squares Finite- Element Solution
of Neutron Transport Problems . . . . . 556--586
F. Hettlich and
W. Rundell A Second Degree Method for Nonlinear
Inverse Problems . . . . . . . . . . . . 587--620
Guo Ben-Yu Gegenbauer Approximation in Certain
Hilbert Spaces and Its Applications to
Singular Differential Equations . . . . 621--645
Françoise Dibos and
Georges Koepfler Global Total Variation Minimization . . 646--664
Gang Bao and
Hongtao Yang A Least-Squares Finite Element Analysis
for Diffraction Problems . . . . . . . . 665--682
E. Dari and
R. G. Durán and
C. Padra Maximum Norm Error Estimators for
Three-Dimensional Elliptic Problems . . 683--700
Carol S. Woodward and
Clint N. Dawson Analysis of Expanded Mixed Finite
Element Methods for a Nonlinear
Parabolic Equation Modeling Flow into
Variably Saturated Porous Media . . . . 701--724
Chun Liu and
Noel J. Walkington Approximation of Liquid Crystal Flows 725--741
Michael Westdickenberg and
Sebastian Noelle A New Convergence Proof for Finite
Volume Schemes Using the Kinetic
Formulation of Conservation Laws . . . . 742--757
So-Hsiang Chou and
Do Y. Kwak Mixed Covolume Methods on Rectangular
Grids For Elliptic Problems . . . . . . 758--771
Mariano Gasca and
Thomas Sauer On Bivariate Hermite Interpolation with
Minimal Degree Polynomials . . . . . . . 772--798
Y. Achdou and
J.-L. Guermond Convergence Analysis of a Finite Element
Projection/Lagrange--Galerkin Method for
the Incompressible Navier--Stokes
Equations . . . . . . . . . . . . . . . 799--826
Andreas Wiegmann and
Kenneth P. Bube The Explicit-Jump Immersed Interface
Method: Finite Difference Methods for
PDEs with Piecewise Smooth Solutions . . 827--862
B. Ben Moussa and
J. P. Vila Convergence of SPH Method for Scalar
Nonlinear Conservation Laws . . . . . . 863--887
Yalchin R. Efendiev and
Thomas Y. Hou and
Xiao-Hui Wu Convergence of a Nonconforming
Multiscale Finite Element Method . . . . 888--910
Qiang Du Convergence Analysis of a Numerical
Method for a Mean Field Model of
Superconducting Vortices . . . . . . . . 911--926
Franz Peherstorfer and
Knut Petras Ultraspherical Gauss--Kronrod Quadrature
Is Not Possible for $ \lambda > 3 $ . . . 927--948
Aaron C. Cinzori and
Patricia K. Lamm Future Polynomial Regularization of
Ill-Posed Volterra Equations . . . . . . 949--979
Kenneth Hvistendahl Karlsen and
Nils Henrik Risebro Corrected Operator Splitting for
Nonlinear Parabolic Equations . . . . . 980--1003
Moody T. Chu A Fast Recursive Algorithm for
Constructing Matrices with Prescribed
Eigenvalues and Singular Values . . . . 1004--1020
Jian Song Deng and
Yu Yu Feng and
Jernej Kozak A Note on the Dimension of the Bivariate
Spline Space over the Morgan--Scott
Triangulation . . . . . . . . . . . . . 1021--1028
Jayadeep Gopalakrishnan and
Joseph E. Pasciak Multigrid for the Mortar Finite Element
Method . . . . . . . . . . . . . . . . . 1029--1052
E. Bécache and
P. Joly and
C. Tsogka An Analysis of New Mixed Finite Elements
for the Approximation of Wave
Propagation Problems . . . . . . . . . . 1053--1084
Faker Ben Belgacem The Mixed Mortar Finite Element Method
for the Incompressible Stokes Problem:
Convergence Analysis . . . . . . . . . . 1085--1100
Houde Han and
Weizhu Bao Error Estimates for the Finite Element
Approximation of Problems in Unbounded
Domains . . . . . . . . . . . . . . . . 1101--1119
T. Shardlow and
A. M. Stuart A Perturbation Theory for Ergodic Markov
Chains and Application to Numerical
Approximations . . . . . . . . . . . . . 1120--1137
Bradley Alpert and
Leslie Greengard and
Thomas Hagstrom Rapid Evaluation of Nonreflecting
Boundary Kernels for Time-Domain Wave
Propagation . . . . . . . . . . . . . . 1138--1164
V. J. Ervin and
W. J. Layton and
J. M. Maubach Adaptive Defect-Correction Methods for
Viscous Incompressible Flow Problems . . 1165--1185
J. M. Peña On the Multivariate Horner Scheme . . . 1186--1197
F. Ben Belgacem Numerical Simulation of Some Variational
Inequalities Arisen from Unilateral
Contact Problems by the Finite Element
Methods . . . . . . . . . . . . . . . . 1198--1216
Lorenzo Pareschi and
Giovanni Russo Numerical Solution of the Boltzmann
Equation I: Spectrally Accurate
Approximation of the Collision Operator 1217--1245
Giovanni Naldi and
Lorenzo Pareschi Numerical Schemes for Hyperbolic Systems
of Conservation Laws with Stiff
Diffusive Relaxation . . . . . . . . . . 1246--1270
Jochen Alberty and
Carsten Carstensen Numerical Analysis of Time-Depending
Primal Elastoplasticity with Hardening 1271--1294
Todd Arbogast and
Lawrence C. Cowsar and
Mary F. Wheeler and
Ivan Yotov Mixed Finite Element Methods on
Nonmatching Multiblock Grids . . . . . . 1295--1315
Hailiang Liu and
Gerald Warnecke Convergence Rates for Relaxation Schemes
Approximating Conservation Laws . . . . 1316--1337
Hong Wang An Optimal-Order Error Estimate for an
ELLAM Scheme for Two-Dimensional Linear
Advection-Diffusion Equations . . . . . 1338--1368
Stephen Wollman On the Approximation of the
Vlasov--Poisson System by Particle
Methods . . . . . . . . . . . . . . . . 1369--1398
Alexander Ostermann and
Cesar Palencia Shadowing for Nonautonomous Parabolic
Problems with Applications to Long-Time
Error Bounds . . . . . . . . . . . . . . 1399--1419
Gabriel J. Lord and
Daniela Peterhof and
Björn Sandstede and
Arnd Scheel Numerical Computation of Solitary Waves
in Infinite Cylindrical Domains . . . . 1420--1454
Max D. Gunzburger and
Hyesuk Kwon Lee An Optimization-Based Domain
Decomposition Method for the
Navier--Stokes Equations . . . . . . . . 1455--1480
M. D. Gunzburger and
S. Manservisi Analysis and Approximation of the
Velocity Tracking Problem for
Navier--Stokes Flows with Distributed
Control . . . . . . . . . . . . . . . . 1481--1512
Qiang Du and
Max D. Gunzburger A Gradient Method Approach to
Optimization-Based Multidisciplinary
Simulations and Nonoverlapping Domain
Decomposition Algorithms . . . . . . . . 1513--1541
Zhiming Chen and
Qiang Du and
Jun Zou Finite Element Methods with Matching and
Nonmatching Meshes for Maxwell Equations
with Discontinuous Coefficients . . . . 1542--1570
Bruce P. Ayati A Variable Time Step Method for an
Age-Dependent Population Model with
Nonlinear Diffusion . . . . . . . . . . 1571--1589
Joe Coyle and
Peter Monk Scattering of Time-Harmonic
Electromagnetic Waves by Anisotropic
Inhomogeneous Scatterers or Impenetrable
Obstacles . . . . . . . . . . . . . . . 1590--1617
Paul Houston and
Christoph Schwab and
Endre Süli Stabilized hp-Finite Element Methods for
First-Order Hyperbolic Problems . . . . 1618--1643
Marie-Noëlle Le Roux Numerical Solution of Nonlinear Reaction
Diffusion Processes . . . . . . . . . . 1644--1656
Barbara I. Wohlmuth and
Andrea Toselli and
Olof B. Widlund An Iterative Substructuring Method for
Raviart--Thomas Vector Fields in Three
Dimensions . . . . . . . . . . . . . . . 1657--1676
Denis Zorin A Method for Analysis of $
{C^1}$-Continuity of Subdivision
Surfaces . . . . . . . . . . . . . . . . 1677--1708
Xiao-Chuan Cai and
Tarek P. Mathew and
Marcus V. Sarkis Maximum Norm Analysis of Overlapping
Nonmatching Grid Discretizations of
Elliptic Equations . . . . . . . . . . . 1709--1728
Avram Sidi The Richardson Extrapolation Process
with a Harmonic Sequence of Collocation
Points . . . . . . . . . . . . . . . . . 1729--1746
X. Q. Liu and
C. W. Li Weak Approximations and Extrapolations
of Stochastic Differential Equations
with Jumps . . . . . . . . . . . . . . . 1747--1767
Christoph Gauger and
Peter Leinen and
Harry Yserentant The Finite Mass Method . . . . . . . . . 1768--1799
Sergej Rjasanow and
Wolfgang Wagner A Temperature Time Counter Scheme for
the Boltzmann Equation . . . . . . . . . 1800--1819
Salim Meddahi and
María González and
Pablo Pérez On a FEM--BEM Formulation for an
Exterior Quasilinear Problem in the
Plane . . . . . . . . . . . . . . . . . 1820--1837
Steinar Evje and
Kenneth Hvistendahl Karlsen Monotone Difference Approximations Of BV
Solutions To Degenerate
Convection-Diffusion Equations . . . . . 1838--1860
Ning Ju Numerical Analysis of Parabolic
$p$-Laplacian: Approximation of
Trajectories . . . . . . . . . . . . . . 1861--1884
Barbara Kaltenbacher A Projection-Regularized Newton Method
for Nonlinear Ill-Posed Problems and Its
Application to Parameter Identification
Problems with Finite Element
Discretization . . . . . . . . . . . . . 1885--1908
Andreas Rieder and
Thomas Schuster The Approximate Inverse in Action with
an Application to Computerized
Tomography . . . . . . . . . . . . . . . 1909--1929
Xiao-liang Cheng On the Nonlinear Inexact Uzawa Algorithm
for Saddle-Point Problems . . . . . . . 1930--1934
Thierry Gallouët and
Rapha\`ele Herbin and
Marie Hél\`ene Vignal Error Estimates on the Approximate
Finite Volume Solution of Convection
Diffusion Equations with General
Boundary Conditions . . . . . . . . . . 1935--1972
Denise Aregba-Driollet and
Roberto Natalini Discrete Kinetic Schemes for
Multidimensional Systems of Conservation
Laws . . . . . . . . . . . . . . . . . . 1973--2004
T. Tachim Medjo Numerical Simulations of a Two-Layer
Quasi-Geostrophic Equation of the Ocean 2005--2022
Philippe G. LeFloch and
Christian Rohde High-Order Schemes, Entropy
Inequalities, and Nonclassical Shocks 2023--2060
Carsten Carstensen and
Petr Plechác Numerical Analysis of Compatible Phase
Transitions in Elastic Solids . . . . . 2061--2081
Salim Meddahi and
Francisco-Javier Sayas A Fully Discrete BEM--FEM for the
Exterior Stokes Problem in the Plane . . 2082--2102
Biyue Liu The Analysis of a Finite Element Method
with Streamline Diffusion for the
Compressible Navier--Stokes Equations 1--16
Xuejun Xu On the Accuracy of Nonconforming
Quadrilateral $ Q^1 $ Element
Approximation for the Navier--Stokes
Problem . . . . . . . . . . . . . . . . 17--39
Masahisa Tabata and
Daisuke Tagami A Finite Element Analysis of a
Linearized Problem of the Navier--Stokes
Equations with Surface Tension . . . . . 40--57
Michael S. Floater and
Ewald G. Quak Linear Independence and Stability of
Piecewise Linear Prewavelets on
Arbitrary Triangulations . . . . . . . . 58--79
Simon Shaw and
J. R. Whiteman Numerical Solution of Linear Quasistatic
Hereditary Viscoelasticity Problems . . 80--97
Eric Darve The fast multipole method. I. Error
analysis and asymptotic complexity . . . 98--128
Robert D. Skeel and
K. Srinivas Nonlinear Stability Analysis of
Area-Preserving Integrators . . . . . . 129--148
Clint N. Dawson and
Mónica L. Martínez-Canales Finite Element Approximations to the
System of Shallow Water Equations, Part
III: On the Treatment of Boundary
Conditions . . . . . . . . . . . . . . . 149--159
Brian R. Wetton Error Analysis of Pressure Increment
Schemes . . . . . . . . . . . . . . . . 160--169
Yao-Lin Jiang and
Omar Wing Monotone Waveform Relaxation for Systems
of Nonlinear Differential-Algebraic
Equations . . . . . . . . . . . . . . . 170--185
Yao-Lin Jiang and
Omar Wing A Note on the Spectra and Pseudospectra
of Waveform Relaxation Operators for
Linear Differential-Algebraic Equations 186--201
A. L. Dontchev and
William W. Hager and
Vladimir M. Veliov Second-Order Runge--Kutta Approximations
in Control Constrained Optimal Control 202--226
Felix C. G. Santos The Linearization Method for the
Numerical Analysis of Finite Element
Solutions to Quasi-linear Elliptic
Partial Differential Equations . . . . . 227--266
A. Bermúdez and
R. G. Durán and
R. Rodríguez and
J. Solomin Finite Element Analysis of a Quadratic
Eigenvalue Problem Arising in
Dissipative Acoustics . . . . . . . . . 267--291
Peter Takác and
Ansgar Jüngel A Nonstiff Euler Discretization of the
Complex Ginzburg--Landau Equation in One
Space Dimension . . . . . . . . . . . . 292--328
W. Govaerts and
Yu. A. Kuznetsov and
B. Sijnave Numerical Methods for the Generalized
Hopf Bifurcation . . . . . . . . . . . . 329--346
P. W. Sharp and
J. H. Verner Some Extended Explicit Bel'tyukov Pairs
for Volterra Integral Equations of the
Second Kind . . . . . . . . . . . . . . 347--359
R. Baker Kearfott and
Jianwei Dian and
A. Neumaier Existence Verification for Singular
Zeros of Complex Nonlinear Systems . . . 360--379
Gabriel N. Gatica and
Norbert Heuer A Dual-Dual Formulation for the Coupling
of Mixed-FEM and BEM in Hyperelasticity 380--400
O. Steinbach Mixed Approximations for Boundary
Elements . . . . . . . . . . . . . . . . 401--413
Ernst Hairer and
Christian Lubich Long-Time Energy Conservation of
Numerical Methods for Oscillatory
Differential Equations . . . . . . . . . 414--441
Christian Ringhofer Space--time Discretization of Series
Expansion Methods for the Boltzmann
Transport Equation . . . . . . . . . . . 442--465
Pedro Morin and
Ricardo H. Nochetto and
Kunibert G. Siebert Data Oscillation and Convergence of
Adaptive FEM . . . . . . . . . . . . . . 466--488
Zhangxin Chen Formulations and Numerical Methods of
the Black Oil Model in Porous Media . . 489--514
Wen-Wei Lin and
Chern-Shuh Wang and
Quan-Fu Xu Numerical Computation of the Minimal $
\mathbf {H}_\infty $ Norm of the
Discrete-Time Output Feedback Control
Problem . . . . . . . . . . . . . . . . 515--547
Weiwei Sun and
Guangwei Yuan Stability Condition for Difference
Schemes for Parabolic Systems . . . . . 548--555
Weimin Han and
Mircea Sofonea Evolutionary Variational Inequalities
Arising in Viscoelastic Contact Problems 556--579
Salvatore Caorsi and
Paolo Fernandes and
Mirco Raffetto On the Convergence of Galerkin Finite
Element Approximations of
Electromagnetic Eigenproblems . . . . . 580--607
Mats G. Larson A Posteriori and a Priori Error Analysis
for Finite Element Approximations of
Self-Adjoint Elliptic Eigenvalue
Problems . . . . . . . . . . . . . . . . 608--625
Sangwoo Heo and
Yuan Xu Invariant Cubature Formulae for Spheres
and Balls by Combinatorial Methods . . . 626--638
Z. Bartoszewski and
M. Kwapisz On Error Estimates for Waveform
Relaxation Methods for
Delay-Differential Equations . . . . . . 639--659
So-Hsiang Chou and
Shengrong Tang Conservative $ P^1 $ Conforming and
Nonconforming Galerkin FEMs: Effective
Flux Evaluation via a Nonmixed Method
Approach . . . . . . . . . . . . . . . . 660--680
John D. Towers Convergence of a Difference Scheme for
Conservation Laws with a Discontinuous
Flux . . . . . . . . . . . . . . . . . . 681--698
Jae Ryong Kweon A Discontinuous Galerkin Method for
Convection-Dominated Compressible
Viscous Navier--Stokes Equations with an
Inflow Boundary Condition . . . . . . . 699--717
Michelle Ghrist and
Bengt Fornberg and
Tobin A. Driscoll Staggered Time Integrators for Wave
Equations . . . . . . . . . . . . . . . 718--741
Zhang Bao-Lin Difference Graphs of Block ADI Method 742--752
Desmond J. Higham Mean-Square and Asymptotic Stability of
the Stochastic Theta Method . . . . . . 753--769
Jichun Li and
Mary F. Wheeler Uniform Convergence and Superconvergence
of Mixed Finite Element Methods on
Anisotropically Refined Grids . . . . . 770--798
Javier de Frutos and
Julia Novo A Spectral Element Method for the
Navier--Stokes Equations with Improved
Accuracy . . . . . . . . . . . . . . . . 799--819
Cesare Davini and
Igino Pitacco An Unconstrained Mixed Method for the
Biharmonic Problem . . . . . . . . . . . 820--836
Dominik Schötzau and
Christoph Schwab Time Discretization of Parabolic
Problems by the HP-Version of the
Discontinuous Galerkin Finite Element
Method . . . . . . . . . . . . . . . . . 837--875
Raymond H. Chan and
Andy M. Yip and
Michael K. Ng The Best Circulant Preconditioners for
Hermitian Toeplitz Systems . . . . . . . 876--896
Torsten Linss and
Hans-Görg Roos and
Relja Vulanovic Uniform Pointwise Convergence on
Shishkin-Type Meshes for Quasi-Linear
Convection-Diffusion Problems . . . . . 897--912
Shi Jin and
Lorenzo Pareschi and
Giuseppe Toscani Uniformly Accurate Diffusive Relaxation
Schemes for Multiscale Transport
Equations . . . . . . . . . . . . . . . 913--936
Tao Lin and
Yanping Lin and
Ming Rao and
Shuhua Zhang Petrov--Galerkin Methods for Linear
Volterra Integro-Differential Equations 937--963
Laurent Gosse and
Charalambos Makridakis Two A Posteriori Error Estimates for
One-Dimensional Scalar Conservation Laws 964--988
Barbara I. Wohlmuth A Mortar Finite Element Method Using
Dual Spaces for the Lagrange Multiplier 989--1012
Yingkang Hu and
Kirill A. Kopotun and
Xiang Ming Yu Modified Adaptive Algorithms . . . . . . 1013--1033
Silvia Bertoluzza and
Claudio Canuto and
Anita Tabacco Stable Discretizations of
Convection-Diffusion Problems via
Computable Negative-Order Inner Products 1034--1055
Do Y. Kwak and
Kwang Y. Kim Mixed Covolume Methods for Quasi-Linear
Second-Order Elliptic Problems . . . . . 1057--1072
Gabriel Acosta and
Ricardo G. Durán Error Estimates for $ {\Cq }_1 $
Isoparametric Elements Satisfying a Weak
Angle Condition . . . . . . . . . . . . 1073--1088
Fred J. Hickernell and
Rong-Xian Yue The Mean Square Discrepancy of Scrambled
$ (t, s)$-Sequences . . . . . . . . . . 1089--1112
Jie Shen Stable and Efficient Spectral Methods in
Unbounded Domains Using Laguerre
Functions . . . . . . . . . . . . . . . 1113--1133
Ilan Bar-On and
Mauro Leoncini Reliable Solution of Tridiagonal Systems
of Linear Equations . . . . . . . . . . 1134--1153
Hailiang Liu and
Jinghua Wang and
Gerald Warnecke The LIP+-Stability and Error Estimates
for a Relaxation Scheme . . . . . . . . 1154--1170
Jiuhua Chen and
Weimin Han and
Mircea Sofonea Numerical Analysis of a Nonlinear
Evolutionary System with Applications in
Viscoplasticity . . . . . . . . . . . . 1171--1199
Xiaojun Chen and
Zuhair Nashed and
Liqun Qi Smoothing Methods and Semismooth Methods
for Nondifferentiable Operator Equations 1200--1216
Chuanju Xu An Efficient Method for the
Navier--Stokes/Euler Coupled Equations
Via a Collocation Approximation . . . . 1217--1242
Matthias Maischak and
Ernst P. Stephan and
Thanh Tran Multiplicative Schwarz Algorithms for
the Galerkin Boundary Element Method . . 1243--1268
Alfred H. Schatz Pointwise Error Estimates and Asymptotic
Error Expansion Inequalities for the
Finite Element Method on Irregular
Grids: Part II. Interior Estimates . . . 1269--1293
Christophe Rabut Multivariate Divided Differences with
Simple Knots . . . . . . . . . . . . . . 1294--1311
Xiaobing Feng Analysis of Finite Element Methods and
Domain Decomposition Algorithms for a
Fluid-Solid Interaction Problem . . . . 1312--1336
Salvatore Fabio Liotta and
Vittorio Romano and
Giovanni Russo Central Schemes for Balance Laws of
Relaxation Type . . . . . . . . . . . . 1337--1356
Raul Kangro and
Roy Nicolaides Far Field Boundary Conditions for
Black--Scholes Equations . . . . . . . . 1357--1368
Laurent O. Jay Inexact Simplified Newton Iterations for
Implicit Runge--Kutta Methods . . . . . 1369--1388
Anne Gelb and
Eitan Tadmor Detection of Edges in Spectral Data II.
Nonlinear Enhancement . . . . . . . . . 1389--1408
B. Le Bailly and
J. P. Thiran Optimal Rational Functions for the
Generalized Zolotarev Problem in the
Complex Plane . . . . . . . . . . . . . 1409--1424
Heping Ma and
Weiwei Sun A Legendre--Petrov--Galerkin and
Chebyshev Collocation Method for
Third-Order Differential Equations . . . 1425--1438
Olga Lepsky Spectral Viscosity Approximations to
Hamilton--Jacobi Solutions . . . . . . . 1439--1453
Sang Dong Kim and
Thomas A. Manteuffel and
Stephen F. McCormick First-Order System Least Squares (FOSLS)
for Spatial Linear Elasticity: Pure
Traction . . . . . . . . . . . . . . . . 1454--1482
Tao Tang and
Zhen-huan Teng On the Regularity of Approximate
Solutions to Conservation Laws with
Piecewise Smooth Solutions . . . . . . . 1483--1495
Giancarlo Sangalli Global and Local Error Analysis for the
Residual-Free Bubbles Method Applied to
Advection-Dominated Problems . . . . . . 1496--1522
R. W. Thatcher A Least Squares Method for Solving
Biharmonic Problems . . . . . . . . . . 1523--1539
Fabio Camilli and
Lars Grüne Numerical Approximation of the Maximal
Solutions for a Class of Degenerate
Hamilton--Jacobi Equations . . . . . . . 1540--1560
Zhiqiang Cai Least Squares for the Perturbed Stokes
Equations and the Reissner--Mindlin
Plate . . . . . . . . . . . . . . . . . 1561--1581
Rakhim Aitbayev and
Bernard Bialecki Orthogonal Spline Collocation for
Nonlinear Dirichlet Problems . . . . . . 1582--1602
Michael Junk A New Perspective on Kinetic Schemes . . 1603--1625
K. Burrage and
P. M. Burrage Order Conditions of Stochastic
Runge--Kutta Methods by $B$-Series . . . 1626--1646
Weinan E and
Xiao-Ping Wang Numerical Methods for the
Landau--Lifshitz Equation . . . . . . . 1647--1665
Scott Kersey Best Near-Interpolation by Curves:
Existence . . . . . . . . . . . . . . . 1666--1675
Paul Castillo and
Bernardo Cockburn and
Ilaria Perugia and
Dominik Schötzau An A Priori Error Analysis of the Local
Discontinuous Galerkin Method for
Elliptic Problems . . . . . . . . . . . 1676--1706
M. A. Taylor and
B. A. Wingate and
R. E. Vincent An Algorithm for Computing Fekete Points
in the Triangle . . . . . . . . . . . . 1707--1720
Mark Ainsworth and
Patrick Coggins The Stability of Mixed hp-Finite
Element Methods for Stokes Flow on High
Aspect Ratio Elements . . . . . . . . . 1721--1761
Willem Hundsdorfer Partially Implicit BDF2 Blends for
Convection Dominated Flows . . . . . . . 1763--1783
Othmar Koch and
Ewa B. Weinmüller Iterated Defect Correction for the
Solution of Singular Initial Value
Problems . . . . . . . . . . . . . . . . 1784--1799
Leon Greenberg and
Marco Marletta Numerical Solution of Non--Self-Adjoint
Sturm--Liouville Problems and Related
Systems . . . . . . . . . . . . . . . . 1800--1845
Hong Wang and
Xiquan Shi and
Richard E. Ewing An ELLAM Scheme for Multidimensional
Advection-Reaction Equations and Its
Optimal-Order Error Estimate . . . . . . 1846--1885
Alexis Vasseur Existence and Properties of Semidiscrete
Shock Profiles for the Isentropic Gas
Dynamic System with $ \gamma = 3 $ . . . 1886--1901
J. Thomas Beale and
Ming-Chih Lai A Method for Computing Nearly Singular
Integrals . . . . . . . . . . . . . . . 1902--1925
Z. Belhachmi and
C. Bernardi and
A. Karageorghis Spectral Element Discretization of the
Circular Driven Cavity, Part II: The
Bilaplacian Equation . . . . . . . . . . 1926--1960
Zhiming Chen and
Shibin Dai Adaptive Galerkin Methods with Error
Control for a Dynamical Ginzburg--Landau
Model in Superconductivity . . . . . . . 1961--1985
Gunilla Kreiss and
Gunilla Efraimsson and
Jan Nordström Elimination of First Order Errors in
Shock Calculations . . . . . . . . . . . 1986--1998
Peter Mathé and
Sergei V. Pereverzev Optimal Discretization of Inverse
Problems in Hilbert Scales.
Regularization and Self-Regularization
of Projection Methods . . . . . . . . . 1999--2021
Andrew J. Sommese and
Jan Verschelde and
Charles W. Wampler Numerical Decomposition of the Solution
Sets of Polynomial Systems into
Irreducible Components . . . . . . . . . 2022--2046
G. Cohen and
P. Joly and
J. E. Roberts and
N. Tordjman Higher Order Triangular Finite Elements
with Mass Lumping for the Wave Equation 2047--2078
Wolfgang Ring A First-Order Sequential
Predictor-Corrector Regularization
Method for Ill-Posed Volterra Equations 2079--2102
F. Malgouyres and
F. Guichard Edge Direction Preserving Image Zooming:
A Mathematical and Numerical Analysis 1--37
María G. Armentano Error Estimates in Sobolev Spaces for
Moving Least Square Approximations . . . 38--51
Ahmed Noussair Riemann Problem with Nonlinear Resonance
Effects and Well-Balanced Godunov Scheme
for Shallow Fluid Flow Past an Obstacle 52--72
Wenbin Liu and
Ningning Yan A Posteriori Error Estimates for Convex
Boundary Control Problems . . . . . . . 73--99
Wenbin Liu and
Ningning Yan Quasi-Norm Local Error Estimators for
$p$-Laplacian . . . . . . . . . . . . . 100--127
Kenth Engò and
Stig Faltinsen Numerical Integration of Lie--Poisson
Systems While Preserving Coadjoint
Orbits and Energy . . . . . . . . . . . 128--145
Andreas Veeser Efficient and Reliable A Posteriori
Error Estimators for Elliptic Obstacle
Problems . . . . . . . . . . . . . . . . 146--167
A. Carpio and
P. Hernando and
M. Kindelan Numerical Study of Hyperbolic Equations
with Integral Constraints Arising in
Semiconductor Theory . . . . . . . . . . 168--191
Barbara I. Wohlmuth and
Rolf H. Krause A Multigrid Method Based on the
Unconstrained Product Space for Mortar
Finite Element Discretizations . . . . . 192--213
Andreas Prohl and
Michael Ruzicka On Fully Implicit Space--time
Discretization for Motions of
Incompressible Fluids with
Shear-Dependent Viscosities: The Case $
p \le 2 $ . . . . . . . . . . . . . . . 214--249
Alexey F. Izmailov and
Vladimir G. Karmanov and
Alexey A. Tretyakov Regularization of Linear Approximate
Schemes by the Gradient Descent . . . . 250--263
Bernardo Cockburn and
Guido Kanschat and
Ilaria Perugia and
Dominik Schötzau Superconvergence of the Local
Discontinuous Galerkin Method for
Elliptic Problems on Cartesian Grids . . 264--285
Zhiqiang Cai and
Seokchan Kim A Finite Element Method Using Singular
Functions for the Poisson Equation:
Corner Singularities . . . . . . . . . . 286--299
Bernhard Beckermann and
Arno B. J. Kuijlaars Superlinear Convergence of Conjugate
Gradients . . . . . . . . . . . . . . . 300--329
Seymour V. Parter Preconditioning Legendre Spectral
Collocation Methods for Elliptic
Problems I: Finite Difference Operators 330--347
Seymour V. Parter Preconditioning Legendre Spectral
Collocation Methods for Elliptic
Problems II: Finite Element Operators 348--362
Ming Wang On the Necessity and Sufficiency of the
Patch Test for Convergence of
Nonconforming Finite Elements . . . . . 363--384
Ansgar Jüngel A Positivity-Preserving Numerical Scheme
for a Nonlinear Fourth Order Parabolic
System . . . . . . . . . . . . . . . . . 385--406
Marko Huhtanen A Matrix Nearness Problem Related to
Iterative Methods . . . . . . . . . . . 407--422
Natalia Kopteva Maximum Norm A Posteriori Error
Estimates for a One-Dimensional
Convection-Diffusion Problem . . . . . . 423--441
Klaus Höllig and
Ulrich Reif and
Joachim Wipper Weighted Extended B-Spline Approximation
of Dirichlet Problems . . . . . . . . . 442--462
Andreas Frommer and
Daniel B. Szyld An Algebraic Convergence Theory for
Restricted Additive Schwarz Methods
Using Weighted Max Norms . . . . . . . . 463--479
Ronald R. Coifman and
Artur Sowa New Methods of Controlled Total
Variation Reduction for Digital
Functions . . . . . . . . . . . . . . . 480--498
Espen Robstad Jakobsen and
Kenneth Hvistendahl Karlsen and
Nils Henrik Risebro On the Convergence Rate of Operator
Splitting for Hamilton--Jacobi Equations
with Source Terms . . . . . . . . . . . 499--518
Chisup Kim and
Raytcho D. Lazarov and
Joseph E. Pasciak and
Panayot S. Vassilevski Multiplier Spaces for the Mortar Finite
Element Method in Three Dimensions . . . 519--538
G. D. Akrivis and
V. A. Dougalis and
G. E. Zouraris Finite Difference Schemes for the
``Parabolic'' Equation in a Variable
Depth Environment with a Rigid Bottom
Boundary Condition . . . . . . . . . . . 539--565
Jochen W. Schmidt and
Marion Bastian and
Bernd Mulansky Nonnegative Volume Matching by Cubic $
C^1 $ Splines on Clough--Tocher Splits 566--586
Xue-Zhang Liang and
Chun-Mei Lü and
Ren-Zhong Feng Properly Posed Sets of Nodes for
Multivariate Lagrange Interpolation in $
C^s $ . . . . . . . . . . . . . . . . . 587--595
Dolores Gómez Pedreira and
Patrick Joly A Method for Computing Guided Waves in
Integrated Optics. Part I: Mathematical
Analysis . . . . . . . . . . . . . . . . 596--623
Frédéric Cao and
Lionel Moisan Geometric Computation of Curvature
Driven Plane Curve Evolutions . . . . . 624--646
C. V. Pao Numerical Methods for Time-Periodic
Solutions of Nonlinear Parabolic
Boundary Value Problems . . . . . . . . 647--667
Gerd Kunert A Local Problem Error Estimator for
Anisotropic Tetrahedral Finite Element
Meshes . . . . . . . . . . . . . . . . . 668--689
R. Bruce Kellogg and
Martin Stynes $n$-Widths and Singularly Perturbed
Boundary Value Problems II . . . . . . . 690--707
Alexander A. Samarskii and
Ivan P. Gavrilyuk and
Vladimir L. Makarov Stability and Regularization of
Three-Level Difference Schemes with
Unbounded Operator Coefficients in
Banach Spaces . . . . . . . . . . . . . 708--723
Sergey Korotov and
Michal Krízek Acute Type Refinements of Tetrahedral
Partitions of Polyhedral Domains . . . . 724--733
Qiang Du and
Benyu Guo and
Jie Shen Fourier Spectral Approximation to a
Dissipative System Modeling the Flow of
Liquid Crystals . . . . . . . . . . . . 735--762
Nicola Guglielmi Asymptotic Stability Barriers for
Natural Runge--Kutta Processes for Delay
Equations . . . . . . . . . . . . . . . 763--783
Serge Nicaise Edge Elements on Anisotropic Meshes and
Approximation of the Maxwell Equations 784--816
Sean Norburn and
David Silvester Fourier Analysis of Stabilized $ Q_1
$--$ Q_1 $ Mixed Finite Element
Approximation . . . . . . . . . . . . . 817--833
Walter Allegretto and
Yanping Lin and
Hongtao Yang Finite Element Error Estimates for a
Nonlocal Problem in American Option
Valuation . . . . . . . . . . . . . . . 834--857
J. Kacur Solution of Degenerate
Convection-Diffusion Problems by the
Method of Characteristics . . . . . . . 858--879
F. Ben Belgacem and
A. Buffa and
Y. Maday The Mortar Finite Element Method for
$3$D Maxwell Equations: First Results 880--901
Béatrice Rivi\`ere and
Mary F. Wheeler and
Vivette Girault A Priori Error Estimates for Finite
Element Methods Based on Discontinuous
Approximation Spaces for Elliptic
Problems . . . . . . . . . . . . . . . . 902--931
Andrea Toselli and
Axel Klawonn A FETI Domain Decomposition Method for
Edge Element Approximations in Two
Dimensions with Discontinuous
Coefficients . . . . . . . . . . . . . . 932--956
Hermann Brunner and
Arvet Pedas and
Gennadi Vainikko Piecewise Polynomial Collocation Methods
for Linear Volterra Integro-Differential
Equations with Weakly Singular Kernels 957--982
Ole H. Hald and
Raz Kupferman Convergence of Optimal Prediction for
Nonlinear Hamiltonian Systems . . . . . 983--1000
Junping Wang and
Xiu Ye Superconvergence of Finite Element
Approximations for the Stokes Problem by
Projection Methods . . . . . . . . . . . 1001--1013
Aihui Zhou An Analysis of Some High Accuracy Finite
Element Methods for Hyperbolic Problems 1014--1028
Martin Burger Iterative Regularization of a Parameter
Identification Problem Occurring in
Polymer Crystallization . . . . . . . . 1029--1055
Qiang Du Optimization Based Nonoverlapping Domain
Decomposition Algorithms and Their
Convergence . . . . . . . . . . . . . . 1056--1077
C. Ringhofer and
C. Schmeiser and
A. Zwirchmayr Moment Methods for the Semiconductor
Boltzmann Equation on Bounded Position
Domains . . . . . . . . . . . . . . . . 1078--1095
Leszek Marcinkowski Domain Decomposition Methods for Mortar
Finite Element Discretizations of Plate
Problems . . . . . . . . . . . . . . . . 1097--1114
Fabiana Leoni Convergence of an Approximation Scheme
for Curvature-Dependent Motions of Sets 1115--1131
Ronald Cools and
Erich Novak Spherical Product Algorithms and the
Integration of Smooth Functions with One
Singular Point . . . . . . . . . . . . . 1132--1145
Francis Filbet Convergence of a Finite Volume Scheme
for the Vlasov--Poisson System . . . . . 1146--1169
So-Hsiang Chou and
Do Y. Kwak and
Kwang Y. Kim A General Framework for Constructing and
Analyzing Mixed Finite Volume Methods on
Quadrilateral Grids: The Overlapping
Covolume Case . . . . . . . . . . . . . 1170--1196
John D. Towers A Difference Scheme for Conservation
Laws with a Discontinuous Flux: The
Nonconvex Case . . . . . . . . . . . . . 1197--1218
C. Buet and
S. Dellacherie and
R. Sentis Numerical Solution of an Ionic
Fokker--Planck Equation with Electronic
Temperature . . . . . . . . . . . . . . 1219--1253
Ben-yu Guo and
He-ping Ma and
Eitan Tadmor Spectral Vanishing Viscosity Method For
Nonlinear Conservation Laws . . . . . . 1254--1268
Marc Küther Error Estimates for the Staggered
Lax--Friedrichs Scheme on Unstructured
Grids . . . . . . . . . . . . . . . . . 1269--1301
Mohammad Majidi and
Gerhard Starke Least-Squares Galerkin Methods for
Parabolic Problems I: Semidiscretization
in Time . . . . . . . . . . . . . . . . 1302--1323
Remi Rocca and
Marius Cocou Numerical Analysis of Quasi-Static
Unilateral Contact Problems with Local
Friction . . . . . . . . . . . . . . . . 1324--1342
Xiaobing Feng and
Ohannes A. Karakashian Two-Level Additive Schwarz Methods for a
Discontinuous Galerkin Approximation of
Second Order Elliptic Problems . . . . . 1343--1365
Uwe Risch Convergence Analysis of the Residual
Free Bubble Method for Bilinear Elements 1366--1379
Heping Ma and
Weiwei Sun Optimal Error Estimates of the
Legendre--Petrov--Galerkin Method for
the Korteweg--de Vries Equation . . . . 1380--1394
Lorenzo Pareschi Central Differencing Based Numerical
Schemes for Hyperbolic Conservation Laws
with Relaxation Terms . . . . . . . . . 1395--1417
Z. Cai and
T. A. Manteuffel and
S. F. McCormick and
J. Ruge First-Order System $ \mathcal {L}
\mathcal {L}^* $ (FOSLL*): Scalar
Elliptic Partial Differential Equations 1418--1445
Natalia Kopteva and
Martin Stynes A Robust Adaptive Method for a
Quasi-Linear One-Dimensional
Convection-Diffusion Problem . . . . . . 1446--1467
Q. Du and
M. Mu and
Z. N. Wu Efficient Parallel Algorithms for
Parabolic Problems . . . . . . . . . . . 1469--1487
Alfio Quarteroni and
Alessandro Veneziani and
Paolo Zunino Mathematical and Numerical Modeling of
Solute Dynamics in Blood Flow and
Arterial Walls . . . . . . . . . . . . . 1488--1511
Ivo Babuska and
Benqi Guo Direct and Inverse Approximation
Theorems for the $p$-Version of the
Finite Element Method in the Framework
of Weighted Besov Spaces. Part I:
Approximability of Functions in the
Weighted Besov Spaces . . . . . . . . . 1512--1538
Ivan Hlavácek Reliable Solution of a Perfect Plastic
Problem with Uncertain Stress-Strain Law
and Yield Function . . . . . . . . . . . 1539--1555
K. W. Morton Discretization of Unsteady Hyperbolic
Conservation Laws . . . . . . . . . . . 1556--1597
John W. Barrett and
James F. Blowey Finite Element Approximation of a
Degenerate Allen--Cahn/Cahn--Hilliard
System . . . . . . . . . . . . . . . . . 1598--1624
T. Tachim Medjo Iterative Methods for a Class of Robust
Control Problems in Fluid Mechanics . . 1625--1647
Mohammad Majidi and
Gerhard Starke Least-Squares Galerkin Methods for
Parabolic Problems II: The Fully
Discrete Case and Adaptive Algorithms 1648--1666
Gerard R. Richter Stable Finite Element Box Methods for
Hyperbolic Equations . . . . . . . . . . 1667--1683
Dolores Gómez Pedreira and
Patrick Joly A Method for Computing Guided Waves in
Integrated Optics. Part II: Numerical
Approximation and Error Analysis . . . . 1684--1711
Xuejun Xu and
Likang Li and
Wenbin Chen A Multigrid Method for the Mortar-Type
Morley Element Approximation of a Plate
Bending Problem . . . . . . . . . . . . 1712--1731
Oleg Davydov and
Larry L. Schumaker Stable Approximation and Interpolation
with $ C^1 $ Quartic Bivariate Splines 1732--1748
Douglas N. Arnold and
Franco Brezzi and
Bernardo Cockburn and
L. Donatella Marini Unified Analysis of Discontinuous
Galerkin Methods for Elliptic Problems 1749--1779
Borislav Bojanov and
Yuan Xu On a Hermite Interpolation by
Polynomials of Two Variables . . . . . . 1780--1793
S. Knapek and
F. Koster Integral Operators on Sparse Grids . . . 1794--1809
I. Bouzoubaa and
K. Hamdache and
A. Noussair A Global Weak Solution via
Transport-Projection Scheme to a Thin
Film Growth Kinetic Model with Nonlocal
Boundary Conditions . . . . . . . . . . 1810--1834
E. O. Ayoola Lagrangian Quadrature Schemes for
Computing Weak Solutions of Quantum
Stochastic Differential Equations . . . 1835--1864
Richard E. Ewing and
Tao Lin and
Yanping Lin On the Accuracy of the Finite Volume
Element Method Based on Piecewise Linear
Polynomials . . . . . . . . . . . . . . 1865--1888
Ping Lin and
Raymond J. Spiteri A Predicted Sequential Regularization
Method for Index-2 Hessenberg DAEs . . . 1889--1913
Mi-Young Kim and
Yonghoon Kwon A Collocation Method for the
Gurtin--MacCamy Equation with Finite
Life-Span . . . . . . . . . . . . . . . 1914--1937
Alan Demlow Suboptimal and Optimal Convergence in
Mixed Finite Element Methods . . . . . . 1938--1953
Markus Bause and
Peter Knabner Uniform Error Analysis for
Lagrange--Galerkin Approximations of
Convection-Dominated Problems . . . . . 1954--1984
Wolfgang Dahmen and
Angela Kunoth and
Reinhold Schneider Wavelet Least Squares Methods for
Boundary Value Problems . . . . . . . . 1985--2013
Ma\"\itine Bergounioux and
Housnaa Zidani A Fully Discrete Approximation for
Control Problems Governed by Parabolic
Variational Inequalities . . . . . . . . 2014--2033
Carsten Carstensen Residual-Based A Posteriori Error
Estimate for a Nonconforming
Reissner--Mindlin Plate Finite Element 2034--2044
Bingkun Li and
Graeme Fairweather and
Bernard Bialecki Discrete-Time Orthogonal Spline
Collocation Methods for Vibration
Problems . . . . . . . . . . . . . . . . 2045--2065
G. N. Milstein and
Yu. M. Repin and
M. V. Tretyakov Symplectic Integration of Hamiltonian
Systems with Additive Noise . . . . . . 2066--2088
Gis\`ele Mophou and
Pascal Poullet A Split Godunov Scheme for Solving
One-Dimensional Hyperbolic Systems in a
Nonconservative Form . . . . . . . . . . 1--25
Christophe Besse and
Brigitte Bidégaray and
Stéphane Descombes Order Estimates in Time of Splitting
Methods for the Nonlinear Schrödinger
Equation . . . . . . . . . . . . . . . . 26--40
R. Hiptmair Symmetric Coupling for Eddy Current
Problems . . . . . . . . . . . . . . . . 41--65
R. Hiptmair and
C. Schwab Natural Boundary Element Methods for the
Electric Field Integral Equation on
Polyhedra . . . . . . . . . . . . . . . 66--86
Erika Hausenblas Error Analysis for Approximation of
Stochastic Differential Equations Driven
by Poisson Random Measures . . . . . . . 87--113
Javier Segura The Zeros of Special Functions from a
Fixed Point Method . . . . . . . . . . . 114--133
IsaÍas Alonso-Mallo and
Nuria Reguera Weak Ill-Posedness of Spatial
Discretizations of Absorbing Boundary
Conditions for Schrödinger-Type Equations 134--158
Axel Klawonn and
Olof B. Widlund and
Maksymilian Dryja Dual-Primal FETI Methods for
Three-Dimensional Elliptic Problems with
Heterogeneous Coefficients . . . . . . . 159--179
K. Arunakirinathar and
B. D. Reddy A Stable Affine-Approximate Finite
Element Method . . . . . . . . . . . . . 180--197
G. C. Hsiao and
P. B. Monk and
N. Nigam Error Analysis of a Finite
Element--Integral Equation Scheme for
Approximating the Time-Harmonic Maxwell
System . . . . . . . . . . . . . . . . . 198--219
Radu Serban and
Linda R. Petzold Efficient Computation of Sensitivities
for Ordinary Differential Equation
Boundary Value Problems . . . . . . . . 220--232
E. Sachs and
S. Volkwein Augmented Lagrange--SQP Methods with
Lipschitz-Continuous Lagrange Multiplier
Updates . . . . . . . . . . . . . . . . 233--253
Howard C. Elman and
Alison Ramage An Analysis of Smoothing Effects of
Upwinding Strategies for the
Convection-Diffusion Equation . . . . . 254--281
K. Chrysafinos and
L. S. Hou Error Estimates for Semidiscrete Finite
Element Approximations of Linear and
Semilinear Parabolic Equations Under
Minimal Regularity Assumptions . . . . . 282--306
Zhiqiang Cai and
Byeong Chun Shin The Discrete First-Order System Least
Squares: The Second-Order Elliptic
Boundary Value Problem . . . . . . . . . 307--318
Bernardo Cockburn and
Guido Kanschat and
Dominik Schötzau and
Christoph Schwab Local Discontinuous Galerkin Methods for
the Stokes System . . . . . . . . . . . 319--343
Zhongying Chen and
Charles A. Micchelli and
Yuesheng Xu Fast Collocation Methods for Second Kind
Integral Equations . . . . . . . . . . . 344--375
L. Formaggia and
J.-F. Gerbeau and
F. Nobile and
A. Quarteroni Numerical Treatment of Defective
Boundary Conditions for the
Navier--Stokes Equations . . . . . . . . 376--401
So-Hsiang Chou and
Do Y. Kwak and
Kwang Y. Kim Flux Recovery from Primal Hybrid Finite
Element Methods . . . . . . . . . . . . 403--415
Klaus Böhmer and
Dása Janovská and
Vladimír Janovský On the Numerical Analysis of the
Imperfect Bifurcation of codim $ \leq 3
$ . . . . . . . . . . . . . . . . . . . 416--430
Arturo Kohatsu-Higa and
Roger Pettersson Variance Reduction Methods for
Simulation of Densities on Wiener Space 431--450
M. Tidriri Convergence Analysis of a Transmission
Algorithm for Convection-Diffusion
Problems . . . . . . . . . . . . . . . . 451--468
Raymond J. Spiteri and
Steven J. Ruuth A New Class of Optimal High-Order
Strong-Stability-Preserving Time
Discretization Methods . . . . . . . . . 469--491
K. Kunisch and
S. Volkwein Galerkin Proper Orthogonal Decomposition
Methods for a General Equation in Fluid
Dynamics . . . . . . . . . . . . . . . . 492--515
Luca Dieci and
Erik S. Van Vleck Lyapunov Spectral Intervals: Theory and
Computation . . . . . . . . . . . . . . 516--542
Li-Qun Cao and
Jun-Zhi Cui and
De-Chao Zhu Multiscale Asymptotic Analysis and
Numerical Simulation for the Second
Order Helmholtz Equations with Rapidly
Oscillating Coefficients Over General
Convex Domains . . . . . . . . . . . . . 543--577
T. Y. Li and
Xiaoshen Wang and
Mengnien Wu Numerical Schubert Calculus by the Pieri
Homotopy Algorithm . . . . . . . . . . . 578--600
Yves Achdou The Mortar Element Method with
Overlapping Subdomains . . . . . . . . . 601--628
K. Engelborghs and
D. Roose On Stability of LMS Methods and
Characteristic Roots of Delay
Differential Equations . . . . . . . . . 629--650
Boris N. Azarenok Variational Barrier Method of Adaptive
Grid Generation in Hyperbolic Problems
of Gas Dynamics . . . . . . . . . . . . 651--682
K. Böhmer and
C. Geiger and
J. D. Rodriguez On a Numerical Liapunov--Schmidt
Spectral Method and Its Application to
Biological Pattern Formation . . . . . . 683--701
Laetitia Paoli and
Michelle Schatzman A Numerical Scheme for Impact Problems
I: The One-Dimensional Case . . . . . . 702--733
Laetitia Paoli and
Michelle Schatzman A Numerical Scheme for Impact Problems
II: The Multidimensional Case . . . . . 734--768
Jue Yan and
Chi-Wang Shu A Local Discontinuous Galerkin Method
for KdV Type Equations . . . . . . . . . 769--791
Chris Perkins A Convergence Analysis of Dykstra's
Algorithm for Polyhedral Sets . . . . . 792--804
Javier de Frutos and
Julia Novo Postprocessing the Linear Finite Element
Method . . . . . . . . . . . . . . . . . 805--819
Daniel Michelson Stability of Discrete Shocks for
Difference Approximations to Systems of
Conservation Laws . . . . . . . . . . . 820--871
Johannes Schropp Geometric Properties of Runge--Kutta
Discretizations for Index $2$
Differential Algebraic Equations . . . . 872--890
A. Klar and
A. Unterreiter Uniform Stability of a Finite Difference
Scheme for Transport Equations in
Diffusive Regimes . . . . . . . . . . . 891--913
Todd F. Dupont and
Yingjie Liu Symmetric Error Estimates for Moving
Mesh Galerkin Methods for
Advection-Diffusion Equations . . . . . 914--927
Sven Beuchler Multigrid Solver for the Inner Problem
in Domain Decomposition Methods for
$p$-FEM . . . . . . . . . . . . . . . . 928--944
Tatsuyuki Nakaki and
Kenji Tomoeda A Finite Difference Scheme for Some
Nonlinear Diffusion Equations in an
Absorbing Medium: Support Splitting
Phenomena . . . . . . . . . . . . . . . 945--964
Mila Nikolova Minimizers of Cost-Functions Involving
Nonsmooth Data-Fidelity Terms.
Application to the Processing of
Outliers . . . . . . . . . . . . . . . . 965--994
V. John and
W. J. Layton Analysis of Numerical Errors in Large
Eddy Simulation . . . . . . . . . . . . 995--1020
Christophe Hazard and
Stephanie Lohrengel A Singular Field Method for Maxwell's
Equations: Numerical Aspects for $2$D
Magnetostatics . . . . . . . . . . . . . 1021--1040
Desmond J. Higham and
Xuerong Mao and
Andrew M. Stuart Strong Convergence of Euler-Type Methods
for Nonlinear Stochastic Differential
Equations . . . . . . . . . . . . . . . 1041--1063
Bruce P. Ayati and
Todd F. Dupont Galerkin Methods in Age and Space for a
Population Model with Nonlinear
Diffusion . . . . . . . . . . . . . . . 1064--1076
George C. Donovan and
Jeffrey S. Geronimo and
Douglas P. Hardin Squeezable Orthogonal Bases: Accuracy
and Smoothness . . . . . . . . . . . . . 1077--1099
Snorre H. Christiansen and
Jean-Claude Nédélec A Preconditioner for the Electric Field
Integral Equation Based on Calderon
Formulas . . . . . . . . . . . . . . . . 1100--1135
Adam Szpiro and
Paul Dupuis Second Order Numerical Methods for First
Order Hamilton--Jacobi Equations . . . . 1136--1183
Ben Schweizer A Stable Time Discretization of the
Stefan Problem with Surface Tension . . 1184--1205
Eberhard Bänsch and
Pedro Morin and
Ricardo H. Nochetto An Adaptive Uzawa FEM for the Stokes
Problem: Convergence without the Inf-Sup
Condition . . . . . . . . . . . . . . . 1207--1229
Stephan Dahlke and
Wolfgang Dahmen and
Karsten Urban Adaptive Wavelet Methods for Saddle
Point Problems --- Optimal Convergence
Rates . . . . . . . . . . . . . . . . . 1230--1262
BjOrn-Ove Heimsund and
Xue-Cheng Tai and
Junping Wang Superconvergence for the Gradient of
Finite Element Approximations by $ L^2 $
Projections . . . . . . . . . . . . . . 1263--1280
Peter A. Markowich and
Paola Pietra and
Carsten Pohl and
Hans Peter Stimming A Wigner-Measure Analysis of the
Dufort--Frankel Scheme for the
Schrödinger Equation . . . . . . . . . . 1281--1310
Gabriel J. Lord and
Jacques Rougemont Topological and \boldmath $ \epsilon
$-Entropy for Large Volume Limits of
Discretized Parabolic Equations . . . . 1311--1329
Boualem Khouider and
Anne Bourlioux Computing the Effective Hamiltonian in
the Majda--Souganidis Model of Turbulent
Premixed Flames . . . . . . . . . . . . 1330--1353
Di-Rong Chen Construction of Smooth Refinable
Function Vectors by Cascade Algorithms 1354--1368
Tony F. Chan and
H. M. Zhou ENO-Wavelet Transforms for Piecewise
Smooth Functions . . . . . . . . . . . . 1369--1404
J. M. Marbán and
C. Palencia A New Numerical Method for Backward
Parabolic Problems in the Maximum-Norm
Setting . . . . . . . . . . . . . . . . 1405--1420
Qiang Du and
Tianyu Zhang Numerical Approximation of Some Linear
Stochastic Partial Differential
Equations Driven by Special Additive
Noises . . . . . . . . . . . . . . . . . 1421--1445
Muruhan Rathinam and
Linda R. Petzold Dynamic Iteration Using Reduced Order
Models: A Method for Simulation of Large
Scale Modular Systems . . . . . . . . . 1446--1474
Amiya K. Pani and
Graeme Fairweather An $ H^1 $-Galerkin Mixed Finite Element
Method for an Evolution Equation with a
Positive-Type Memory Term . . . . . . . 1475--1490
Zhangxin Chen and
Richard E. Ewing and
Qiaoyuan Jiang and
Anna M. Spagnuolo Error Analysis for Characteristics-Based
Methods for Degenerate Parabolic
Problems . . . . . . . . . . . . . . . . 1491--1515
Kevin Burrage and
Tianhai Tian Predictor-Corrector Methods of
Runge--Kutta Type for Stochastic
Differential Equations . . . . . . . . . 1516--1537
Richard E. Ewing and
Yanping Lin and
Tong Sun and
Junping Wang and
Shuhua Zhang Sharp $ L^2 $-Error Estimates and
Superconvergence of Mixed Finite Element
Methods for Non-Fickian Flows in Porous
Media . . . . . . . . . . . . . . . . . 1538--1560
Mohamed Amara and
Daniela Capatina-Papaghiuc and
Amna Chatti New Locking-Free Mixed Method for the
Reissner--Mindlin Thin Plate Model . . . 1561--1582
G. N. Milstein and
Yu. M. Repin and
M. V. Tretyakov Numerical Methods for Stochastic Systems
Preserving Symplectic Structure . . . . 1583--1604
Kent Andre Mardal and
Xue-Cheng Tai and
Ragnar Winther A Robust Finite Element Method for
Darcy--Stokes Flow . . . . . . . . . . . 1605--1631
Mohamed Amara and
Daniela Capatina-Papaghiuc and
Amna Chatti Bending Moment Mixed Method for the
Kirchhoff--Love Plate Model . . . . . . 1632--1649
I. H. Sloan and
F. Y. Kuo and
S. Joe Constructing Randomly Shifted Lattice
Rules in Weighted Sobolev Spaces . . . . 1650--1665
John P. Boyd Computing Zeros on a Real Interval
through Chebyshev Expansion and
Polynomial Rootfinding . . . . . . . . . 1666--1682
Weimin Han and
Lie-heng Wang Nonconforming Finite Element Analysis
for a Plate Contact Problem . . . . . . 1683--1697
Eleanor W. Jenkins and
Ba'eatrice Rivia`ere and
Mary F. Wheeler A Priori Error Estimates for Mixed
Finite Element Approximations of the
Acoustic Wave Equation . . . . . . . . . 1698--1715
Karl Oelschläger Simulation of the Solution of a Viscous
Porous Medium Equation by a Particle
Method . . . . . . . . . . . . . . . . . 1716--1762
Guang-Ze Gu and
Dong-Hui Li and
Liqun Qi and
Shu-Zi Zhou Descent Directions of Quasi-Newton
Methods for Symmetric Nonlinear
Equations . . . . . . . . . . . . . . . 1763--1774
Martin Burger and
Wolfram Mühlhuber Numerical Approximation of an SQP-Type
Method for Parameter Identification . . 1775--1797
Daniele Bertaccini The Spectrum of Circulant-Like
Preconditioners for Some General Linear
Multistep Formulas for Linear Boundary
Value Problems . . . . . . . . . . . . . 1798--1822
Alfredo Bermúdez and
Rodolfo Rodríguez and
Pilar Salgado A Finite Element Method with Lagrange
Multipliers for Low-Frequency Harmonic
Maxwell Equations . . . . . . . . . . . 1823--1849
Wenbin Liu and
Ningning Yan A Posteriori Error Estimates for Control
Problems Governed by Stokes Equations 1850--1869
Wenbin Liu and
Ningning Yan On Quasi-Norm Interpolation Error
Estimation And A Posteriori Error
Estimates for $p$-Laplacian . . . . . . 1870--1895
Micha Janssen and
Pascal Van Hentenryck and
Yves Deville A Constraint Satisfaction Approach for
Enclosing Solutions to Parametric
Ordinary Differential Equations . . . . 1896--1939
Heinz-Otto Kreiss and
N. Anders Petersson and
Jacob Yström Difference Approximations for the Second
Order Wave Equation . . . . . . . . . . 1940--1967
P. G. LeFloch and
J. M. Mercier and
C. Rohde Fully Discrete, Entropy Conservative
Schemes of Arbitrary Order . . . . . . . 1968--1992
Thomas Apel and
Joachim Schöberl Multigrid Methods for Anisotropic Edge
Refinement . . . . . . . . . . . . . . . 1993--2006
Thierry Goudon Analysis of a Semidiscrete Version of
the Wigner Equation . . . . . . . . . . 2007--2025
Andrew J. Sommese and
Jan Verschelde and
Charles W. Wampler Symmetric Functions Applied to
Decomposing Solution Sets of Polynomial
Systems . . . . . . . . . . . . . . . . 2026--2046
Mark Ainsworth and
Katia Pinchedez \em hp-Approximation Theory for BDFM and
RT Finite Elements on Quadrilaterals . . 2047--2068
Elena Celledoni and
Brynjulf Owren A Class of Intrinsic Schemes for
Orthogonal Integration . . . . . . . . . 2069--2084
Luminita A. Vese and
Stanley J. Osher Numerical Methods for $p$-Harmonic Flows
and Applications to Image Processing . . 2085--2104
Yong-Jung Kim Piecewise Self-Similar Solutions and a
Numerical Scheme for Scalar Conservation
Laws . . . . . . . . . . . . . . . . . . 2105--2132
Richard E. Ewing and
Mingjun Liu and
Junping Wang A New Superconvergence for Mixed Finite
Element Approximations . . . . . . . . . 2133--2150
Clint Dawson The $ {\cal P}^k + 1 - {\cal S}^k $
Local Discontinuous Galerkin Method for
Elliptic Equations . . . . . . . . . . . 2151--2170
Dominik Schötzau and
Christoph Schwab and
Andrea Toselli Mixed \em hp-DGFEM for Incompressible
Flows . . . . . . . . . . . . . . . . . 2171--2194
William J. Layton and
Friedhelm Schieweck and
Ivan Yotov Coupling Fluid Flow with Porous Media
Flow . . . . . . . . . . . . . . . . . . 2195--2218
Valeria Simoncini and
Daniel B. Szyld Flexible Inner-Outer Krylov Subspace
Methods . . . . . . . . . . . . . . . . 2219--2239
Roberto Ferretti Convergence of Semi-Lagrangian
Approximations to Convex
Hamilton--Jacobi Equations under (Very)
Large Courant Numbers . . . . . . . . . 2240--2253
M. S. Min and
D. Gottlieb On the Convergence of the Fourier
Approximation for Eigenvalues and
Eigenfunctions of Discontinuous Problems 2254--2269
Yingjie Liu and
Randolph E. Bank and
Todd F. Dupont and
Sonia Garcia and
Rafael F. Santos Symmetric Error Estimates for Moving
Mesh Mixed Methods for
Advection-Diffusion Equations . . . . . 2270--2291
Rapha\`ele Herbin A Monotonic Method for the Numerical
Solution of Some Free Boundary Value
Problems . . . . . . . . . . . . . . . . 2292--2310
James S. Ball Half-Range Generalized Hermite
Polynomials and the Related Gaussian
Quadratures . . . . . . . . . . . . . . 2311--2317
Reinhard Nabben and
Daniel B. Szyld Convergence Theory of Restricted
Multiplicative Schwarz Methods . . . . . 2318--2336
Yuzhi Cai Convergence Theory of a Numerical Method
for Solving the Chapman--Kolmogorov
Equation . . . . . . . . . . . . . . . . 2337--2351
Defeng Sun and
Jie Sun Strong Semismoothness of Eigenvalues of
Symmetric Matrices and Its Application
to Inverse Eigenvalue Problems . . . . . 2352--2367
C. Bernardi and
T. Chacon Rebollo and
R. Lewandowski and
F. Murat A Model for Two Coupled Turbulent Fluids
Part II: Numerical Analysis of a
Spectral Discretization . . . . . . . . 2368--2394
B. N. Khoromskij and
J. M. Melenk Boundary Concentrated Finite Element
Methods . . . . . . . . . . . . . . . . 1--36
Eric T. Chung and
Qiang Du and
Jun Zou Convergence Analysis of a Finite Volume
Method for Maxwell's Equations in
Nonhomogeneous Media . . . . . . . . . . 37--63
Christian Ringhofer A Mixed Spectral-Difference Method for
the Steady State Boltzmann--Poisson
System . . . . . . . . . . . . . . . . . 64--89
Andrew Lumsdaine and
Deyun Wu Krylov Subspace Acceleration of Waveform
Relaxation . . . . . . . . . . . . . . . 90--111
J. L. Guermond and
Jie Shen Velocity-Correction Projection Methods
for Incompressible Flows . . . . . . . . 112--134
François Bouchut and
Shi Jin and
Xiantao Li Numerical Approximations of Pressureless
and Isothermal Gas Dynamics . . . . . . 135--158
T. von Petersdorff and
C. Schwab Wavelet Discretizations of Parabolic
Integrodifferential Equations . . . . . 159--180
Z. Cai and
R. R. Parashkevov and
T. F. Russell and
J. D. Wilson and
X. Ye Domain Decomposition for a Mixed Finite
Element Method in Three Dimensions . . . 181--194
Andrei Bourchtein and
Vladimir Kadychnikov Well Posedness of the Initial Value
Problem for Vertically Discretized
Hydrostatic Equations . . . . . . . . . 195--207
Stephen Roberts and
Markus Hegland and
Irfan Altas Approximation of a Thin Plate Spline
Smoother Using Continuous Piecewise
Polynomial Functions . . . . . . . . . . 208--234
Weiming Cao and
Ricardo Carretero-González and
Weizhang Huang and
Robert D. Russell Variational Mesh Adaptation Methods for
Axisymmetrical Problems . . . . . . . . 235--257
E. Ovtchinnikov Convergence Estimates for the
Generalized Davidson Method for
Symmetric Eigenvalue Problems I: The
Preconditioning Aspect . . . . . . . . . 258--271
E. Ovtchinnikov Convergence Estimates for the
Generalized Davidson Method for
Symmetric Eigenvalue Problems II: The
Subspace Acceleration . . . . . . . . . 272--286
Sergey Asvadurov and
Vladimir Druskin and
Murthy N. Guddati and
Leonid Knizhnerman On Optimal Finite-Difference
Approximation of PML . . . . . . . . . . 287--305
Susanne C. Brenner Poincaré--Friedrichs Inequalities for
Piecewise $ H^1 $ Functions . . . . . . 306--324
James A. Sethian and
Alexander Vladimirsky Ordered Upwind Methods for Static
Hamilton--Jacobi Equations: Theory and
Algorithms . . . . . . . . . . . . . . . 325--363
Yanzhao Cao and
Terry Herdman and
Yuesheng Xu A Hybrid Collocation Method for Volterra
Integral Equations with Weakly Singular
Kernels . . . . . . . . . . . . . . . . 364--381
K. Guittet On the Time-Continuous Mass Transport
Problem and Its Approximation by
Augmented Lagrangian Techniques . . . . 382--399
E. J. Doedel and
W. Govaerts and
Yu. A. Kuznetsov Computation of Periodic Solution
Bifurcations in ODEs Using Bordered
Systems . . . . . . . . . . . . . . . . 401--435
Petr Knobloch and
Lutz Tobiska The $ P_1^\protect \lowercasemod $
Element: A New Nonconforming Finite
Element for Convection-Diffusion
Problems . . . . . . . . . . . . . . . . 436--456
Vincent J. Ervin and
William W. Miles Approximation of Time-Dependent
Viscoelastic Fluid Flow: SUPG
Approximation . . . . . . . . . . . . . 457--486
Huazhong Tang and
Tao Tang Adaptive Mesh Methods for One- and
Two-Dimensional Hyperbolic Conservation
Laws . . . . . . . . . . . . . . . . . . 487--515
Bosko S. Jovanovic and
Lubin G. Vulkov On the Convergence of Difference Schemes
for Hyperbolic Problems with
Concentrated Data . . . . . . . . . . . 516--538
Robert Eymard and
Thierry Gallouët H-Convergence and Numerical Schemes for
Elliptic Problems . . . . . . . . . . . 539--562
Francis Filbet and
Philippe Laurençot Numerical Approximation of the
Lifshitz--Slyozov--Wagner Equation . . . 563--588
Rakhim Aitbayev and
Bernard Bialecki A Preconditioned Conjugate Gradient
Method for Nonselfadjoint or Indefinite
Orthogonal Spline Collocation Problems 589--604
Willem Hundsdorfer and
Steven J. Ruuth and
Raymond J. Spiteri Monotonicity-Preserving Linear Multistep
Methods . . . . . . . . . . . . . . . . 605--623
Chunjae Park and
Dongwoo Sheen $ P_1 $-Nonconforming Quadrilateral
Finite Element Methods for Second-Order
Elliptic Problems . . . . . . . . . . . 624--640
Laurent Gosse and
Giuseppe Toscani Space Localization and Well-Balanced
Schemes for Discrete Kinetic Models in
Diffusive Regimes . . . . . . . . . . . 641--658
Hua Wu and
Heping Ma and
Huiyuan Li Optimal Error Estimates of the
Chebyshev--Legendre Spectral Method for
Solving the Generalized Burgers Equation 659--672
Yen-Hsi Richard Tsai and
Li-Tien Cheng and
Stanley Osher and
Hong-Kai Zhao Fast Sweeping Algorithms for a Class of
Hamilton--Jacobi Equations . . . . . . . 673--694
Len G. Margolin and
Edriss S. Titi and
Shannon Wynne The Postprocessing Galerkin and
Nonlinear Galerkin Methods---A
Truncation Analysis Point of View . . . 695--714
Zhiqiang Cai and
Gerhard Starke First-Order System Least Squares for the
Stress-Displacement Formulation: Linear
Elasticity . . . . . . . . . . . . . . . 715--730
Mark Ainsworth and
Joe Coyle Conditioning of Hierarchic $p$-Version
Nédélec Elements on Meshes of Curvilinear
Quadrilaterals and Hexahedra . . . . . . 731--750
Yuan Xu Polynomial Interpolation on the Unit
Sphere . . . . . . . . . . . . . . . . . 751--766
Sang Dong Kim and
Seymour V. Parter Semicirculant Preconditioning of
Elliptic Operators . . . . . . . . . . . 767--795
Qiang Du and
Benyu Guo and
Jie Shen Corrigendum: ``Fourier spectral
approximation to a dissipative system
modeling the flow of liquid crystals
[SIAM J. Numer. Anal. \bf 39 (2001), no.
3, 735--762 (electronic); MR1860443
(2002g:76006)] . . . . . . . . . . . . . 796--798
Zhiming Chen and
Haijun Wu An Adaptive Finite Element Method with
Perfectly Matched Absorbing Layers for
the Wave Scattering by Periodic
Structures . . . . . . . . . . . . . . . 799--826
Amparo Gil and
Javier Segura Computing the Zeros and Turning Points
of Solutions of Second Order Homogeneous
Linear ODEs . . . . . . . . . . . . . . 827--855
Carl de Boor A Leibniz Formula for Multivariate
Divided Differences . . . . . . . . . . 856--868
Andreas Rieder and
Adel Faridani The Semidiscrete Filtered Backprojection
Algorithm Is Optimal for Tomographic
Inversion . . . . . . . . . . . . . . . 869--892
Marsha J. Berger and
Christiane Helzel and
Randall J. LeVeque $ {H}$-Box Methods for the Approximation
of Hyperbolic Conservation Laws on
Irregular Grids . . . . . . . . . . . . 893--918
R. Hiptmair Coupling of Finite Elements and Boundary
Elements in Electromagnetic Scattering 919--944
Marlis Hochbruck and
Christian Lubich On Magnus Integrators for Time-Dependent
Schrödinger Equations . . . . . . . . . . 945--963
Qingping Deng An Optimal Parallel Nonoverlapping
Domain Decomposition Iterative Procedure 964--982
Richard E. Groff and
Pramod P. Khargonekar and
Daniel E. Koditschek A Local Convergence Proof for the Minvar
Algorithm for Computing Continuous
Piecewise Linear Approximations . . . . 983--1007
J. Frédéric Bonnans and
Housnaa Zidani Consistency of Generalized Finite
Difference Schemes for the Stochastic
HJB Equation . . . . . . . . . . . . . . 1008--1021
J. M. Peña Scaled Pivots and Scaled Partial
Pivoting Strategies . . . . . . . . . . 1022--1031
Charalambos Makridakis and
Beno\^\it Perthame Sharp CFL, Discrete Kinetic Formulation,
and Entropic Schemes for Scalar
Conservation Laws . . . . . . . . . . . 1032--1051
Lori Badea and
Xue-Cheng Tai and
Junping Wang Convergence Rate Analysis of a
Multiplicative Schwarz Method for
Variational Inequalities . . . . . . . . 1052--1073
Rob Stevenson Adaptive Solution of Operator Equations
Using Wavelet Frames . . . . . . . . . . 1074--1100
Yanren Hou and
Kaitai Li A Small Eddy Correction Method for
Nonlinear Dissipative Evolutionary
Equations . . . . . . . . . . . . . . . 1101--1130
Stefano Micheletti and
Simona Perotto and
Marco Picasso Stabilized Finite Elements on
Anisotropic Meshes: A Priori Error
Estimates for the Advection-Diffusion
and the Stokes Problems . . . . . . . . 1131--1162
Roger Samelson and
Roger Temam and
Cheng Wang and
Shouhong Wang Surface Pressure Poisson Equation
Formulation of the Primitive Equations:
Numerical Schemes . . . . . . . . . . . 1163--1194
L. Demkowicz and
I. Babuska $p$ Interpolation Error Estimates for
Edge Finite Elements of Variable Order
in Two Dimensions . . . . . . . . . . . 1195--1208
Xiao-Chuan Cai and
Maksymilian Dryja and
Marcus Sarkis Restricted Additive Schwarz
Preconditioners with Harmonic Overlap
for Symmetric Positive Definite Linear
Systems . . . . . . . . . . . . . . . . 1209--1231
E. Cuesta and
C. Palencia A Numerical Method for an
Integro-Differential Equation with
Memory in Banach Spaces: Qualitative
Properties . . . . . . . . . . . . . . . 1232--1241
János Karátson and
István Faragó Variable Preconditioning via
Quasi-Newton Methods for Nonlinear
Problems in Hilbert Space . . . . . . . 1242--1262
Yinnian He Two-Level Method Based on Finite Element
and Crank--Nicolson Extrapolation for
the Time-Dependent Navier--Stokes
Equations . . . . . . . . . . . . . . . 1263--1285
Claude-Henri Lamarque and
Jérôme Bastien and
Matthieu Holland Study of a Maximal Monotone Model with a
Delay Term . . . . . . . . . . . . . . . 1286--1300
Anthony Michel A Finite Volume Scheme for Two-Phase
Immiscible Flow in Porous Media . . . . 1301--1317
Hongsen Chen and
Junping Wang An Interior Estimate of Superconvergence
for Finite Element Solutions for
Second-Order Elliptic Problems on
Quasi-uniform Meshes by Local
Projections . . . . . . . . . . . . . . 1318--1338
Steve Bryson and
Doron Levy High-Order Central WENO Schemes for
Multidimensional Hamilton--Jacobi
Equations . . . . . . . . . . . . . . . 1339--1369
Sang Dong Kim and
Hyung-Chun Lee and
Byeong Chun Shin Pseudospectral Least-Squares Method for
the Second-Order Elliptic Boundary Value
Problem . . . . . . . . . . . . . . . . 1370--1387
Arnold Reusken Convergence Analysis of the
Gauss--Seidel Preconditioner for
Discretized One Dimensional Euler
Equations . . . . . . . . . . . . . . . 1388--1405
Weizhu Bao and
Dieter Jaksch An Explicit Unconditionally Stable
Numerical Method for Solving Damped
Nonlinear Schrödinger Equations with a
Focusing Nonlinearity . . . . . . . . . 1406--1426
John W. Barrett and
Harald Garcke and
Robert Nürnberg Finite Element Approximation of
Surfactant Spreading on a Thin Film . . 1427--1464
F. Y. Kuo and
S. Joe Component-By-Component Construction of
Good Intermediate-Rank Lattice Rules . . 1465--1486
M. I. M. Copetti and
D. A. French Numerical Solution of a
Thermoviscoelastic Contact Problem by a
Penalty Method . . . . . . . . . . . . . 1487--1504
Francesca Rapetti and
François Dubois Discrete Vector Potentials for Nonsimply
Connected Three-Dimensional Domains . . 1505--1527
Giancarlo Sangalli Quasi Optimality of the SUPG Method for
the One-Dimensional Advection-Diffusion
Problem . . . . . . . . . . . . . . . . 1528--1542
Philipp Kügler Identification of a Temperature
Dependent Heat Conductivity from Single
Boundary Measurements . . . . . . . . . 1543--1563
Jörg Büttner and
Bernd Simeon Time Integration of the Dual Problem of
Elastoplasticity by Runge--Kutta Methods 1564--1584
Charalambos Makridakis and
Ricardo H. Nochetto Elliptic Reconstruction and a Posteriori
Error Estimates for Parabolic Problems 1585--1594
Jie Shen A New Dual-Petrov--Galerkin Method for
Third and Higher Odd-Order Differential
Equations: Application to the KDV
Equation . . . . . . . . . . . . . . . . 1595--1619
Martin Stynes and
Lutz Tobiska The SDFEM for a Convection-Diffusion
Problem with a Boundary Layer: Optimal
Error Analysis and Enhancement of
Accuracy . . . . . . . . . . . . . . . . 1620--1642
Martin J. Gander and
Laurence Halpern and
Frédéric Nataf Optimal Schwarz Waveform Relaxation for
the One Dimensional Wave Equation . . . 1643--1681
Qiya Hu and
Jun Zou A Nonoverlapping Domain Decomposition
Method for Maxwell's Equations in Three
Dimensions . . . . . . . . . . . . . . . 1682--1708
Bernard Bialecki and
Maksymilian Dryja A Nonoverlapping Domain Decomposition
Method for Orthogonal Spline Collocation
Problems . . . . . . . . . . . . . . . . 1709--1728
Salim Meddahi and
Antonio Márquez and
Virginia Selgas Computing Acoustic Waves in an
Inhomogeneous Medium of the Plane by a
Coupling of Spectral and Finite Elements 1729--1750
Ricardo G. Durán and
Erwin Hernández and
Luis Hervella-Nieto and
Elsa Liberman and
Rodolfo Rodríguez Error Estimates for Low-Order
Isoparametric Quadrilateral Finite
Elements for Plates . . . . . . . . . . 1751--1772
Om Prakash Agrawal and
John Gregory $ O(h^2) $ Global Pointwise Algorithms
for Delay Quadratic Problems in the
Calculus of Variations . . . . . . . . . 1773--1784
Albert Cohen and
Wolfgang Dahmen Adaptive Wavelet Schemes for Nonlinear
Variational Problems . . . . . . . . . . 1785--1823
Isaias Alonso-Mallo and
Nuria Reguera Discrete Absorbing Boundary Conditions
for Schrödinger-Type Equations.
Construction and Error Analysis . . . . 1824--1850
Natalia Kopteva Error Expansion for an Upwind Scheme
Applied to a Two-Dimensional
Convection-Diffusion Problem . . . . . . 1851--1869
G. Mastroianni and
G. Monegato Truncated Quadrature Rules Over $ (0,
\infty) $ and Nyström-Type Methods . . . 1870--1892
Muruhan Rathinam and
Linda R. Petzold A New Look at Proper Orthogonal
Decomposition . . . . . . . . . . . . . 1893--1925
James Glimm and
Xiaolin Li and
Yingjie Liu and
Zhiliang Xu and
Ning Zhao Conservative Front Tracking with
Improved Accuracy . . . . . . . . . . . 1926--1947
Wayne B. Hayes and
Kenneth R. Jackson Rigorous Shadowing of Numerical
Solutions of Ordinary Differential
Equations by Containment . . . . . . . . 1948--1973
Gabriel N. Gatica and
Helmut Harbrecht and
Reinhold Schneider Least Squares Methods for the Coupling
of FEM and BEM . . . . . . . . . . . . . 1974--1995
Jérôme Droniou and
Thierry Gallouët and
Rapha\`ele Herbin A Finite Volume Scheme for a Noncoercive
Elliptic Equation with Measure Data . . 1997--2031
Francesca Fierro and
Andreas Veeser A Posteriori Error Estimators for
Regularized Total Variation of
Characteristic Functions . . . . . . . . 2032--2055
W. Guo and
L. S. Hou Generalizations and Accelerations of
Lions' Nonoverlapping Domain
Decomposition Method for Linear Elliptic
PDE . . . . . . . . . . . . . . . . . . 2056--2080
Houde Han and
Xiaonan Wu A Fast Numerical Method for the
Black--Scholes Equation of American
Options . . . . . . . . . . . . . . . . 2081--2095
Lars Grüne Attraction Rates, Robustness, and
Discretization of Attractors . . . . . . 2096--2113
Huo-Yuan Duan and
Guo-Ping Liang On the Velocity-Pressure-Vorticity
Least-Squares Mixed Finite Element
Method for the $3$D Stokes Equations . . 2114--2130
Malin Siklosi and
Gunilla Kreiss Elimination of First Order Errors in
Time Dependent Shock Calculations . . . 2131--2148
Alfred H. Schatz and
Lars B. Wahlbin Pointwise Error Estimates for
Differences in Piecewise Linear Finite
Element Approximations . . . . . . . . . 2149--2160
Klaus Deckelnick and
Gerhard Dziuk and
Charles M. Elliott Error Analysis of a Semidiscrete
Numerical Scheme for Diffusion in
Axially Symmetric Surfaces . . . . . . . 2161--2179
Jukka Sarvas Performing Interpolation and
Anterpolation Entirely by Fast Fourier
Transform in the $3$-D Multilevel Fast
Multipole Algorithm . . . . . . . . . . 2180--2196
A. L. Codd and
T. A. Manteuffel and
S. F. McCormick Multilevel First-Order System Least
Squares for Nonlinear Elliptic Partial
Differential Equations . . . . . . . . . 2197--2209
A. L. Codd and
T. A. Manteuffel and
S. F. McCormick and
J. W. Ruge Multilevel First-Order System Least
Squares for Elliptic Grid Generation . . 2210--2232
Rémi Abgrall Numerical Discretization of Boundary
Conditions for First Order
Hamilton--Jacobi Equations . . . . . . . 2233--2261
Anthony Michel and
Julien Vovelle Entropy Formulation for Parabolic
Degenerate Equations with General
Dirichlet Boundary Conditions and
Application to the Convergence of FV
Methods . . . . . . . . . . . . . . . . 2262--2293
Randolph E. Bank and
Jinchao Xu Asymptotically Exact A Posteriori Error
Estimators, Part I: Grids with
Superconvergence . . . . . . . . . . . . 2294--2312
Randolph E. Bank and
Jinchao Xu Asymptotically Exact A Posteriori Error
Estimators, Part II: General
Unstructured Grids . . . . . . . . . . . 2313--2332
Weizhang Huang and
Heping Ma and
Weiwei Sun Convergence Analysis of Spectral
Collocation Methods for a Singular
Differential Equation . . . . . . . . . 2333--2349
R. Baker Kearfott and
Jianwei Dian Existence Verification for Higher Degree
Singular Zeros of Nonlinear Systems . . 2350--2373
Ohannes A. Karakashian and
Frederic Pascal A Posteriori Error Estimates for a
Discontinuous Galerkin Approximation of
Second-Order Elliptic Problems . . . . . 2374--2399
Q. Du and
M. D. Gunzburger and
L. S. Hou and
J. Lee Semidiscrete Finite Element
Approximations of a Linear
Fluid-Structure Interaction Problem . . 1--29
David M. Sloan On the Norms of Inverses of
Pseudospectral Differentiation Matrices 30--48
Weiying Zheng and
Lung-an Ying Finite Element Approximations to the
Discrete Spectrum of the Schrödinger
Operator with the Coulomb Potential . . 49--74
Carsten Carstensen and
Georg Dolzmann Time-Space Discretization of the
Nonlinear Hyperbolic System $ u_t t =
\operatorname {div} (\sigma (D u) + D
u_t) $ . . . . . . . . . . . . . . . . . 75--89
Jayadeep Gopalakrishnan and
Joseph E. Pasciak and
Leszek F. Demkowicz Analysis of a Multigrid Algorithm for
Time Harmonic Maxwell Equations . . . . 90--108
Hyesuk Lee A Multigrid Method for Viscoelastic
Fluid Flow . . . . . . . . . . . . . . . 109--129
Barry Lee and
Stephen F. McCormick and
Bobby Philip and
Daniel J. Quinlan Asynchronous Fast Adaptive
Composite-Grid Methods for Elliptic
Problems: Theoretical Foundations . . . 130--152
A. A. Dosiyev The High Accurate Block-Grid Method for
Solving Laplace's Boundary Value Problem
with Singularities . . . . . . . . . . . 153--178
Adimurthi and
Jérôme Jaffré and
G. D. Veerappa Gowda Godunov-Type Methods for Conservation
Laws with a Flux Function Discontinuous
in Space . . . . . . . . . . . . . . . . 179--208
Nicolas Victoir Asymmetric Cubature Formulae with Few
Points in High Dimension for Symmetric
Measures . . . . . . . . . . . . . . . . 209--227
Boris A. Andreianov and
Michaël Gutnic and
Petra Wittbold Convergence of Finite Volume
Approximations for a Nonlinear
Elliptic-Parabolic Problem: A
``Continuous'' Approach . . . . . . . . 228--251
Mats G. Larson and
A. Jonas Niklasson Analysis of a Nonsymmetric Discontinuous
Galerkin Method for Elliptic Problems:
Stability and Energy Error Estimates . . 252--264
Bernhard A. Schmitt and
Rüdiger Weiner Parallel Two-Step $W$-Methods with Peer
Variables . . . . . . . . . . . . . . . 265--282
Bernardo Cockburn and
Jayadeep Gopalakrishnan A Characterization of Hybridized Mixed
Methods for Second Order Elliptic
Problems . . . . . . . . . . . . . . . . 283--301
T. Tachim Medjo and
L. R. Tcheugoue Tebou Adjoint-Based Iterative Method for
Robust Control Problems in Fluid
Mechanics . . . . . . . . . . . . . . . 302--325
Jie Shen and
Li-Lian Wang Error Analysis for Mapped Legendre
Spectral and Pseudospectral Methods . . 326--349
Nicolas Besse Convergence of a Semi-Lagrangian Scheme
for the One-Dimensional Vlasov--Poisson
System . . . . . . . . . . . . . . . . . 350--382
Hermann Schichl and
Arnold Neumaier Exclusion Regions for Systems of
Equations . . . . . . . . . . . . . . . 383--408
E. Bécache and
A.-S. Bonnet-Ben Dhia and
G. Legendre Perfectly Matched Layers for the
Convected Helmholtz Equation . . . . . . 409--433
Paul Houston and
Ilaria Perugia and
Dominik Schotzau Mixed Discontinuous Galerkin
Approximation of the Maxwell Operator 434--459
H. R. MacMillan and
T. A. Manteuffel and
S. F. McCormick First-Order System Least Squares and
Electrical Impedance Tomography . . . . 461--483
Bruno Després An Explicit A Priori Estimate for a
Finite Volume Approximation of Linear
Advection on Non-Cartesian Grids . . . . 484--504
Sören Bartels Adaptive Approximation of Young Measure
Solutions in Scalar Nonconvex
Variational Problems . . . . . . . . . . 505--529
S. Blanes and
F. Casas and
A. Murua On the Numerical Integration of Ordinary
Differential Equations by Processed
Methods . . . . . . . . . . . . . . . . 531--552
Mark Ainsworth Discrete Dispersion Relation for
hp-Version Finite Element
Approximation at High Wave Number . . . 553--575
Todd Arbogast Analysis of a Two-Scale, Locally
Conservative Subgrid Upscaling for
Elliptic Problems . . . . . . . . . . . 576--598
J. Thomas Beale A Grid-Based Boundary Integral Method
for Elliptic Problems in Three
Dimensions . . . . . . . . . . . . . . . 599--620
A. Buffa and
R. Hiptmair A Coercive Combined Field Integral
Equation for Electromagnetic Scattering 621--640
Qiang Zhang and
Chi-Wang Shu Error Estimates to Smooth Solutions of
Runge--Kutta Discontinuous Galerkin
Methods for Scalar Conservation Laws . . 641--666
Faker Ben Belgacem A Stabilized Domain Decomposition Method
with Nonmatching Grids for the Stokes
Problem in Three Dimensions . . . . . . 667--685
Gabriele Steidl and
Joachim Weickert and
Thomas Brox and
Pavel Mrázek and
Martin Welk On the Equivalence of Soft Wavelet
Shrinkage, Total Variation Diffusion,
Total Variation Regularization, and
SIDEs . . . . . . . . . . . . . . . . . 686--713
J. L. Guermond A Finite Element Technique for Solving
First-Order PDEs in \em L$^p$ . . . . . 714--737
John W. Barrett and
Robert Nürnberg and
Vanessa Styles Finite Element Approximation of a Phase
Field Model for Void Electromigration 738--772
Eberhard Bänsch and
Pedro Morin and
Ricardo H. Nochetto Surface Diffusion of Graphs: Variational
Formulation, Error Analysis, and
Simulation . . . . . . . . . . . . . . . 773--799
Ivo Babuska and
Raúl Tempone and
Georgios E. Zouraris Galerkin Finite Element Approximations
of Stochastic Elliptic Partial
Differential Equations . . . . . . . . . 800--825
Zhiqiang Cai and
Gerhard Starke Least-Squares Methods for Linear
Elasticity . . . . . . . . . . . . . . . 826--842
Zhiqiang Cai and
Barry Lee and
Ping Wang Least-Squares Methods for Incompressible
Newtonian Fluid Flow: Linear Stationary
Problems . . . . . . . . . . . . . . . . 843--859
Martin Berggren Approximations of Very Weak Solutions to
Boundary-Value Problems . . . . . . . . 860--877
Jesús Palacián Integration of Perturbed Initial Value
Problems through Reduction Theory . . . 878--904
Qiya Hu and
Zhongci Shi and
Dehao Yu Efficient Solvers for Saddle-Point
Problems Arising from Domain
Decompositions with Lagrange Multipliers 905--933
Christophe Besse A Relaxation Scheme for the Nonlinear
Schrödinger Equation . . . . . . . . . . 934--952
Jernej Kozak and
Emil Zagar On Geometric Interpolation by Polynomial
Curves . . . . . . . . . . . . . . . . . 953--967
Peter Mathé Saturation of Regularization Methods for
Linear Ill-Posed Problems in Hilbert
Spaces . . . . . . . . . . . . . . . . . 968--973
Steven J. Ruuth and
Raymond J. Spiteri High-Order Strong-Stability-Preserving
Runge--Kutta Methods with
Downwind-Biased Spatial Discretizations 974--996
Jong-Shi Pang and
Thomas P.-Y. Yu Continuous $M$-Estimators and Their
Interpolation by Polynomials . . . . . . 997--1017
Yao-Lin Jiang On Time-Domain Simulation of Lossless
Transmission Lines with Nonlinear
Terminations . . . . . . . . . . . . . . 1018--1031
Wenbin Liu and
Heping Ma and
Tao Tang and
Ningning Yan A Posteriori Error Estimates for
Discontinuous Galerkin Time-Stepping
Method for Optimal Control Problems
Governed by Parabolic Equations . . . . 1032--1061
Xiu Ye A New Discontinuous Finite Volume Method
for Elliptic Problems . . . . . . . . . 1062--1072
L. Ferracina and
M. N. Spijker Stepsize Restrictions for the
Total-Variation-Diminishing Property in
General Runge--Kutta Methods . . . . . . 1073--1093
Lishang Jiang and
Min Dai Convergence of Binomial Tree Methods for
European/American Path-Dependent Options 1094--1109
Dmitry E. Pelinovsky and
Yury A. Stepanyants Convergence of Petviashvili's Iteration
Method for Numerical Approximation of
Stationary Solutions of Nonlinear Wave
Equations . . . . . . . . . . . . . . . 1110--1127
Gilles Aubert and
Laure Blanc-Féraud and
Riccardo March $ {\Gamma } $-Convergence of Discrete
Functionals with Nonconvex Perturbation
for Image Classification . . . . . . . . 1128--1145
Zhangxin Chen and
Hongsen Chen Pointwise Error Estimates of
Discontinuous Galerkin Methods with
Penalty for Second-Order Elliptic
Problems . . . . . . . . . . . . . . . . 1146--1166
Penny J. Davies and
Dugald B. Duncan Stability and Convergence of Collocation
Schemes for Retarded Potential Integral
Equations . . . . . . . . . . . . . . . 1167--1188
Pavel Bochev and
Max Gunzburger An Absolutely Stable Pressure-Poisson
Stabilized Finite Element Method for the
Stokes Equations . . . . . . . . . . . . 1189--1207
J.-C. Latché and
D. Vola Analysis of the Brezzi--Pitkäranta
Stabilized Galerkin Scheme for Creeping
Flows of Bingham Fluids . . . . . . . . 1208--1225
Michael Plexousakis and
Georgios E. Zouraris On the Construction and Analysis of High
Order Locally Conservative Finite
Volume-Type Methods for One-Dimensional
Elliptic Problems . . . . . . . . . . . 1226--1260
Maxim A. Olshanskii and
Arnold Reusken Convergence Analysis of a Multigrid
Method for a Convection-Dominated Model
Problem . . . . . . . . . . . . . . . . 1261--1291
Heinz-Otto Kreiss and
N. Anders Petersson and
Jacob Yström Difference Approximations of the Neumann
Problem for the Second Order Wave
Equation . . . . . . . . . . . . . . . . 1292--1323
C. M. Elliott and
D. Kay and
V. Styles A Finite Element Approximation of a
Variational Inequality Formulation of
Bean's Model for Superconductivity . . . 1324--1341
Sven Beuchler Multilevel Solvers for a Finite Element
Discretization of a Degenerate Problem 1342--1356
Christos Arvanitis and
Charalambos Makridakis and
Athanasios E. Tzavaras Stability and Convergence of a Class of
Finite Element Schemes for Hyperbolic
Systems of Conservation Laws . . . . . . 1357--1393
R. Luce and
B. I. Wohlmuth A Local A Posteriori Error Estimator
Based on Equilibrated Fluxes . . . . . . 1394--1414
Olivier Gibaru Tensorial Rational Surfaces with Base
Points via Massic Vectors . . . . . . . 1415--1434
Sergey Repin and
Stefan Sauter and
Anton Smolianski A Posteriori Estimation of Dimension
Reduction Errors for Elliptic Problems
on Thin Domains . . . . . . . . . . . . 1435--1451
Florin Radu and
Iuliu Sorin Pop and
Peter Knabner Order of Convergence Estimates for an
Euler Implicit, Mixed Finite Element
Discretization of Richards' Equation . . 1452--1478
Albert Cohen and
Marc Hoffmann and
Markus Reiss Adaptive Wavelet Galerkin Methods for
Linear Inverse Problems . . . . . . . . 1479--1501
Daniele Boffi and
Lucia Gastaldi Analysis of Finite Element Approximation
of Evolution Problems in Mixed Form . . 1502--1526
Jérémie Szeftel Design of Absorbing Boundary Conditions
for Schrödinger Equations in $ \mathbb
{R}^d $ . . . . . . . . . . . . . . . . 1527--1551
Andrew J. Sommese and
Jan Verschelde and
Charles W. Wampler Homotopies for Intersecting Solution
Components of Polynomial Systems . . . . 1552--1571
L. Beirao da Veiga Finite Element Methods for a Modified
Reissner--Mindlin Free Plate Model . . . 1572--1591
Tri Van and
Aihua Wood A Time-Domain Finite Element Method for
Maxwell's Equations . . . . . . . . . . 1592--1609
A. M. Sauer-Budge and
J. Bonet and
A. Huerta and
J. Peraire Computing Bounds for Linear Functionals
of Exact Weak Solutions to Poisson's
Equation . . . . . . . . . . . . . . . . 1610--1630
R. Nabben and
C. Vuik A Comparison of Deflation and Coarse
Grid Correction Applied to Porous Media
Flow . . . . . . . . . . . . . . . . . . 1631--1647
René Pinnau Uniform Convergence of an Exponentially
Fitted Scheme for the Quantum Drift
Diffusion Model . . . . . . . . . . . . 1648--1668
Robert D. Falgout and
Panayot S. Vassilevski On Generalizing the Algebraic Multigrid
Framework . . . . . . . . . . . . . . . 1669--1693
M. Torrilhon and
M. Fey Constraint-Preserving Upwind Methods for
Multidimensional Advection Equations . . 1694--1728
Liping Liu and
Tang Liu and
Michal Krízek and
Tao Lin and
Shuhua Zhang Global Superconvergence and A Posteriori
Error Estimators of the Finite Element
Method for a Quasi-linear Elliptic
Boundary Value Problem of Nonmonotone
Type . . . . . . . . . . . . . . . . . . 1729--1744
Zhi-Qiang Wang and
Jianxin Zhou A Local Minimax-Newton Method for
Finding Multiple Saddle Points with
Symmetries . . . . . . . . . . . . . . . 1745--1759
Xiaoqun Wang and
Ian H. Sloan and
Josef Dick On Korobov Lattice Rules in Weighted
Spaces . . . . . . . . . . . . . . . . . 1760--1779
Ahmed Naga and
Zhimin Zhang A Posteriori Error Estimates Based on
the Polynomial Preserving Recovery . . . 1780--1800
Noel J. Walkington Convergence of the Discontinuous
Galerkin Method for Discontinuous
Solutions . . . . . . . . . . . . . . . 1801--1817
Mirco Raffetto Discrete Compactness for Edge Elements
in the Presence of Mixed Boundary
Conditions . . . . . . . . . . . . . . . 1818--1829
Martin Weiser and
Anton Schiela and
Peter Deuflhard Asymptotic Mesh Independence of Newton's
Method Revisited . . . . . . . . . . . . 1830--1845
Jason Cantarella On Comparing the Writhe of a Smooth
Curve to the Writhe of an Inscribed
Polygon . . . . . . . . . . . . . . . . 1846--1861
S. B. Yuste and
L. Acedo An Explicit Finite Difference Method and
a New von Neumann-Type Stability
Analysis for Fractional Diffusion
Equations . . . . . . . . . . . . . . . 1862--1874
Omar Lakkis and
Ricardo H. Nochetto A Posteriori Error Analysis for the Mean
Curvature Flow of Graphs . . . . . . . . 1875--1898
Xiao-song Qian and
Cheng-long Xu and
Li-shang Jiang and
Bao-jun Bian Convergence of the Binomial Tree Method
for American Options in a Jump-Diffusion
Model . . . . . . . . . . . . . . . . . 1899--1913
Todd Arbogast and
Mary F. Wheeler A Family of Rectangular Mixed Elements
with a Continuous Flux for Second Order
Elliptic Problems . . . . . . . . . . . 1914--1931
P. Chatzipantelidis and
R. D. Lazarov Error Estimates for a Finite Volume
Element Method for Elliptic PDEs in
Nonconvex Polygonal Domains . . . . . . 1932--1958
Béatrice Rivi\`ere and
Ivan Yotov Locally Conservative Coupling of Stokes
and Darcy Flows . . . . . . . . . . . . 1959--1977
Sergei Konyagin and
Bojan Popov and
Ognian Trifonov On Convergence of Minmod-Type Schemes 1978--1997
Leszek Marcinkowski A Mortar Finite Element Method for
Fourth Order Problems in Two Dimensions
with Lagrange Multipliers . . . . . . . 1998--2019
Chengming Huang and
Stefan Vandewalle Discretized Stability and Error Growth
of The Nonautonomous Pantograph Equation 2020--2042
Claudio Canuto and
Karsten Urban Adaptive Optimization of Convex
Functionals in Banach Spaces . . . . . . 2043--2075
Yahia Lebbah and
Claude Michel and
Michel Rueher and
David Daney and
Jean-Pierre Merlet Efficient and Safe Global Constraints
for Handling Numerical Constraint
Systems . . . . . . . . . . . . . . . . 2076--2097
Olivier Bokanowski and
Mohammed Lemou Fast Multipole Method for Multivariable
Integrals . . . . . . . . . . . . . . . 2098--2117
Ricardo H. Nochetto and
Kunibert G. Siebert and
Andreas Veeser Fully Localized A Posteriori Error
Estimators and Barrier Sets for Contact
Problems . . . . . . . . . . . . . . . . 2118--2135
Carsten Carstensen Estimation of Higher Sobolev Norm from
Lower Order Approximation . . . . . . . 2136--2147
Jörg Liesen and
Paul E. Saylor Orthogonal Hessenberg Reduction and
Orthogonal Krylov Subspace Bases . . . . 2148--2158
Hyea Hyun Kim and
Chang-Ock Lee A Preconditioner for the FETI-DP
Formulation with Mortar Methods in Two
Dimensions . . . . . . . . . . . . . . . 2159--2175
S. C. Reddy and
J. A. C. Weideman The Accuracy of the Chebyshev
Differencing Method for Analytic
Functions . . . . . . . . . . . . . . . 2176--2187
Rob Stevenson An Optimal Adaptive Finite Element
Method . . . . . . . . . . . . . . . . . 2188--2217
Arieh Iserles and
Antonella Zanna Efficient Computation of the Matrix
Exponential by Generalized Polar
Decompositions . . . . . . . . . . . . . 2218--2256
Brian D. Ewald and
Roger Témam Numerical Analysis of Stochastic Schemes
in Geophysics . . . . . . . . . . . . . 2257--2276
Peter Kunkel and
Volker Mehrmann and
Ronald Stöver Multiple Shooting for Unstructured
Nonlinear Differential-Algebraic
Equations of Arbitrary Index . . . . . . 2277--2297
Oscar P. Bruno and
E. McKay Hyde Higher-Order Fourier Approximation in
Scattering by Two-Dimensional,
Inhomogeneous Media . . . . . . . . . . 2298--2319
Mark Ainsworth Robust A Posteriori Error Estimation for
Nonconforming Finite Element
Approximation . . . . . . . . . . . . . 2320--2341
Alfred H. Schatz Perturbations of Forms and Error
Estimates for the Finite Element Method
at a Point, with an Application to
Improved Superconvergence Error
Estimates for Subspaces that Are
Symmetric with Respect to a Point . . . 2342--2365
Winfried Auzinger and
Othmar Koch and
Ewa Weinmüller Analysis of a New Error Estimate for
Collocation Methods Applied to Singular
Boundary Value Problems . . . . . . . . 2366--2386
Gerhard Starke A First-Order System Least Squares
Finite Element Method for the Shallow
Water Equations . . . . . . . . . . . . 2387--2407
Habib Ammari and
Hyeonbae Kang and
Eunjoo Kim and
Mikyoung Lim Reconstruction of Closely Spaced Small
Inclusions . . . . . . . . . . . . . . . 2408--2428
Douglas N. Arnold and
Daniele Boffi and
Richard S. Falk Quadrilateral $ \boldmath H $ (div)
Finite Elements . . . . . . . . . . . . 2429--2451
Mohammad Majidi Least-Squares Galerkin Methods for
Parabolic Problems III: Semidiscrete
Case for Semilinear Problems . . . . . . 2452--2475
Barbara I. Wohlmuth A $ \cal V $-cycle Multigrid Approach
for Mortar Finite Elements . . . . . . . 2476--2495
C. Carstensen and
R. Lazarov and
S. Tomov Explicit and Averaging A Posteriori
Error Estimates for Adaptive Finite
Volume Methods . . . . . . . . . . . . . 2496--2521
Gerald Moore Floquet Theory as a Computational Tool 2522--2568
Guido Giese Nonlinear Stability Analysis for the
Method of Transport for the
Elastic-Plastic Wave Equation . . . . . 2569--2589
Andrea Toselli and
Xavier Vasseur Dual-Primal FETI Algorithms for Edge
Element Approximations: Two-Dimensional
$H$ And $P$ Finite Elements on
Shape-Regular Meshes . . . . . . . . . . 2590--2611
Chiu-Yen Kao and
Stanley Osher and
Yen-Hsi Tsai Fast Sweeping Methods for Static
Hamilton--Jacobi Equations . . . . . . . 2612--2632
Carsten Carstensen and
Dirk Praetorius Numerical Analysis for a Macroscopic
Model in Micromagnetics . . . . . . . . 2633--2651
Richards Grzhibovskis and
Alexei Heintz A Convolution-Thresholding Approximation
of Generalized Curvature Flows . . . . . 2652--2670
Pierre Degond and
Shi Jin A Smooth Transition Model between
Kinetic and Diffusion Equations . . . . 2671--2687
C. Lovadina A Low-order Nonconforming Finite Element
for Reissner--Mindlin Plates . . . . . . 2688--2705
Annalisa Buffa Remarks on the Discretization of Some
Noncoercive Operator with Applications
to Heterogeneous Maxwell Equations . . . 1--18
Weiming Cao On the Error of Linear Interpolation and
the Orientation, Aspect Ratio, and
Internal Angles of a Triangle . . . . . 19--40
Francesc Arandiga and
Albert Cohen and
Rosa Donat and
Nira Dyn Interpolation and Approximation of
Piecewise Smooth Functions . . . . . . . 41--57
Heping Ma and
Weiwei Sun and
Tao Tang Hermite Spectral Methods with a
Time-Dependent Scaling for Parabolic
Equations in Unbounded Domains . . . . . 58--75
Josef Dick and
Gunther Leobacher and
Friedrich Pillichshammer Construction Algorithms for Digital Nets
with Low Weighted Star Discrepancy . . . 76--95
Z. Dostál Inexact Semimonotonic Augmented
Lagrangians with Optimal Feasibility
Convergence for Convex Bound and
Equality Constrained Quadratic
Programming . . . . . . . . . . . . . . 96--115
Snorre H. Christiansen A Div-Curl Lemma for Edge Elements . . . 116--126
J. M. Melenk \em hp-Interpolation of Nonsmooth
Functions and an Application to \em hp
--- A posteriori Error Estimation . . . 127--155
S. Hüeber and
B. I. Wohlmuth An Optimal A Priori Error Estimate for
Nonlinear Multibody Contact Problems . . 156--173
F. Saleri and
A. Veneziani Pressure Correction Algebraic Splitting
Methods for the Incompressible
Navier--Stokes Equations . . . . . . . . 174--194
Shuyu Sun and
Mary F. Wheeler Symmetric and Nonsymmetric Discontinuous
Galerkin Methods for Reactive Transport
in Porous Media . . . . . . . . . . . . 195--219
Sören Bartels Stability and Convergence of
Finite-Element Approximation Schemes for
Harmonic Maps . . . . . . . . . . . . . 220--238
J. L. Guermond and
P. Minev and
J. Shen Error Analysis of Pressure-Correction
Schemes for the Time-Dependent Stokes
Equations with Open Boundary Conditions 239--258
Rick Archibald and
Anne Gelb and
Jungho Yoon Polynomial Fitting for Edge Detection in
Irregularly Sampled Signals and Images 259--279
Paola Causin and
Riccardo Sacco A Discontinuous Petrov--Galerkin Method
with Lagrangian Multipliers for Second
Order Elliptic Problems . . . . . . . . 280--302
Eric T. Chung and
Bjorn Engquist Convergence Analysis of Fully Discrete
Finite Volume Methods for Maxwell's
Equations in Nonhomogeneous Media . . . 303--317
Johannes Korsawe and
Gerhard Starke A Least-Squares Mixed Finite Element
Method for Biot's Consolidation Problem
in Porous Media . . . . . . . . . . . . 318--339
Pavel Bochev and
Max Gunzburger On Least-Squares Finite Element Methods
for the Poisson Equation and Their
Connection to the Dirichlet and Kelvin
Principles . . . . . . . . . . . . . . . 340--362
Sören Bartels Reliable and Efficient Approximation of
Polyconvex Envelopes . . . . . . . . . . 363--385
Markus Berndt and
Thomas A. Manteuffel and
Stephen F. McCormick and
Gerhard Starke Analysis of First-Order System Least
Squares (FOSLS) for Elliptic Problems
with Discontinuous Coefficients: Part I 386--408
Markus Berndt and
Thomas A. Manteuffel and
Stephen F. McCormick Analysis of First-Order System Least
Squares (FOSLS) for Elliptic Problems
with Discontinuous Coefficients: Part II 409--436
Sidi Mahmoud Kaber and
Yvon Maday Analysis of Some Padé--Chebyshev
Approximants . . . . . . . . . . . . . . 437--454
Ángel Balaguer and
Carlos Conde Fourth-Order Nonoscillatory Upwind and
Central Schemes for Hyperbolic
Conservation Laws . . . . . . . . . . . 455--473
R. Eymard and
T. Gallouët and
V. Gervais and
R. Masson Convergence of a Numerical Scheme for
Stratigraphic Modeling . . . . . . . . . 474--501
M. S. Min and
D. Gottlieb Domain Decomposition Spectral
Approximations for an Eigenvalue Problem
with a Piecewise Constant Coefficient 502--520
Jiangguo Liu and
Bojan Popov and
Hong Wang and
Richard E. Ewing Convergence Analysis of Wavelet Schemes
for Convection-Reaction Equations under
Minimal Regularity Assumptions . . . . . 521--539
Guy Barles and
Espen R. Jakobsen Error Bounds for Monotone Approximation
Schemes for Hamilton--Jacobi--Bellman
Equations . . . . . . . . . . . . . . . 540--558
Siddhartha Mishra Convergence of Upwind Finite Difference
Schemes for a Scalar Conservation Law
with Indefinite Discontinuities in the
Flux Function . . . . . . . . . . . . . 559--577
Daniel Bouche and
Jean-Michel Ghidaglia and
Frédéric Pascal Error Estimate and the Geometric
Corrector for the Upwind Finite Volume
Method Applied to the Linear Advection
Equation . . . . . . . . . . . . . . . . 578--603
Andreas Rieder Inexact Newton Regularization Using
Conjugate Gradients as Inner Iteration 604--622
Jie Shen and
Li-Lian Wang Spectral Approximation of the Helmholtz
Equation with High Wave Numbers . . . . 623--644
Zhiming Chen and
Xuezhe Liu An Adaptive Perfectly Matched Layer
Technique for Time-harmonic Scattering
Problems . . . . . . . . . . . . . . . . 645--671
Malin Siklosi and
Gunilla Efraimsson Analysis of First Order Errors in Shock
Calculations in Two Space Dimensions . . 672--685
Rakhim Aitbayev Multilevel Preconditioners for
Non--self-adjoint or Indefinite
Orthogonal Spline Collocation Problems 686--706
S. Dekel and
D. Leviatan Adaptive Multivariate Approximation
Using Binary Space Partitions and
Geometric Wavelets . . . . . . . . . . . 707--732
Rajen Kumar Sinha and
Bhupen Deka Optimal Error Estimates for Linear
Parabolic Problems with Discontinuous
Coefficients . . . . . . . . . . . . . . 733--749
Rodrigo B. Platte and
Tobin A. Driscoll Polynomials and Potential Theory for
Gaussian Radial Basis Function
Interpolation . . . . . . . . . . . . . 750--766
F. Frühauf and
O. Scherzer and
A. Leitão Analysis of Regularization Methods for
the Solution of Ill-Posed Problems
Involving Discontinuous Operators . . . 767--786
Borislav Bojanov and
Petar Petrov Gaussian Interval Quadrature Formulae
for Tchebycheff Systems . . . . . . . . 787--795
Dietmar Kröner and
Mai Duc Thanh Numerical Solutions to Compressible
Flows in a Nozzle with Variable
Cross-section . . . . . . . . . . . . . 796--824
Patrick Joly and
Jerónimo Rodriguez An Error Analysis of Conservative
Space--time Mesh Refinement Methods for
the One-Dimensional Wave Equation . . . 825--859
L. Saas and
I. Faille and
F. Nataf and
F. Willien Finite Volume Methods for Domain
Decomposition on Nonmatching Grids with
Arbitrary Interface Conditions . . . . . 860--890
Zhi-Qiang Wang and
Jianxin Zhou An Efficient and Stable Method for
Computing Multiple Saddle Points with
Symmetries . . . . . . . . . . . . . . . 891--907
Allal Guessab and
Gerhard Schmeisser Sharp Error Estimates for Interpolatory
Approximation on Convex Polytopes . . . 909--923
Inmaculada Higueras Representations of Runge--Kutta Methods
and Strong Stability Preserving Methods 924--948
Manfred Dobrowolski and
Manuel Villegas A Stabilized Mixed Finite Element Method
for Elliptic Systems of First Order . . 949--969
Michael Breuss The Implicit Upwind Method for $1$-D
Scalar Conservation Laws with Continuous
Fluxes . . . . . . . . . . . . . . . . . 970--986
Holger Wendland On the Convergence of a General Class of
Finite Volume Methods . . . . . . . . . 987--1002
Fred J. Hickernell and
Ian H. Sloan and
Grzegorz W. Wasilkowski A Piecewise Constant Algorithm for
Weighted $ L_1 $ Approximation over
Bounded or Unbounded Regions in $ \R^s $ 1003--1020
Mary F. Wheeler and
Ivan Yotov A Posteriori Error Estimates for the
Mortar Mixed Finite Element Method . . . 1021--1042
Ricardo H. Nochetto and
Jae-Hong Pyo The Gauge--Uzawa Finite Element Method.
Part I: The Navier--Stokes Equations . . 1043--1068
Marlis Hochbruck and
Alexander Ostermann Explicit Exponential Runge--Kutta
Methods for Semilinear Parabolic
Problems . . . . . . . . . . . . . . . . 1069--1090
Blanca Ayuso and
Bosco García-Archilla and
Julia Novo The Postprocessed Mixed Finite-Element
Method for the Navier--Stokes Equations 1091--1111
Klaus Deckelnick and
Gerhard Dziuk and
Charles M. Elliott Fully Discrete Finite Element
Approximation for Anisotropic Surface
Diffusion of Graphs . . . . . . . . . . 1112--1138
G. N. Milstein and
M. V. Tretyakov Numerical Integration of Stochastic
Differential Equations with Nonglobally
Lipschitz Coefficients . . . . . . . . . 1139--1154
V. Simoncini Variable Accuracy of Matrix-Vector
Products in Projection Methods for
Eigencomputation . . . . . . . . . . . . 1155--1174
Sofiane Soussi Convergence of the Supercell Method for
Defect Modes Calculations in Photonic
Crystals . . . . . . . . . . . . . . . . 1175--1201
B. D. Bonner and
I. G. Graham and
V. P. Smyshlyaev The Computation of Conical Diffraction
Coefficients in High-Frequency Acoustic
Wave Scattering . . . . . . . . . . . . 1202--1230
Jan Nordström and
Magnus Svärd Well-Posed Boundary Conditions for the
Navier--Stokes Equations . . . . . . . . 1231--1255
Emmanuel Gobet and
Sylvain Maire Sequential Control Variates for
Functionals of Markov Processes . . . . 1256--1275
Xuejun Xu and
R. H. W. Hoppe On the Convergence of Mortar Edge
Element Methods in $ \R^3 $ . . . . . . 1276--1294
Z. Belhachmi and
J. M. Sac-Epée and
J. Sokolowski Mixed Finite Element Methods for Smooth
Domain Formulation of Crack Problems . . 1295--1320
Brett W. Bader Tensor-Krylov Methods for Solving
Large-Scale Systems of Nonlinear
Equations . . . . . . . . . . . . . . . 1321--1347
Andreas Frommer and
Bruno Lang Existence Tests for Solutions of
Nonlinear Equations Using Borsuk's
Theorem . . . . . . . . . . . . . . . . 1348--1361
Yubin Yan Galerkin Finite Element Methods for
Stochastic Parabolic Partial
Differential Equations . . . . . . . . . 1363--1384
K. R. Fowler and
C. T. Kelley Pseudo-Transient Continuation for
Nonsmooth Nonlinear Equations . . . . . 1385--1406
Yu. A. Kuznetsov and
W. Govaerts and
E. J. Doedel and
A. Dhooge Numerical Periodic Normalization for
Codim $1$ Bifurcations of Limit Cycles 1407--1435
Morgan Pierre Weak Series \em BV Convergence of a
Moving Finite-Element Method for
Singular Axisymmetric Harmonic Maps . . 1436--1454
Jeongho Ahn and
David E. Stewart An Euler--Bernoulli Beam with Dynamic
Contact: Discretization, Convergence,
and Numerical Results . . . . . . . . . 1455--1480
Serge Nicaise A Posteriori Error Estimations of Some
Cell-Centered Finite Volume Methods . . 1481--1503
Jianli Xie and
Jun Zou Numerical Reconstruction of Heat Fluxes 1504--1535
Jorge San Martín and
Jean-François Scheid and
Takéo Takahashi and
Marius Tucsnak Convergence of the Lagrange--Galerkin
Method for the Equations Modelling the
Motion of a Fluid-Rigid System . . . . . 1536--1571
Songul Kaya and
Béatrice Rivi\`ere A Discontinuous Subgrid Eddy Viscosity
Method for the Time-Dependent
Navier--Stokes Equations . . . . . . . . 1572--1595
Rama Cont and
Ekaterina Voltchkova A Finite Difference Scheme for Option
Pricing in Jump Diffusion and
Exponential Lévy Models . . . . . . . . . 1596--1626
Bernardo Cockburn and
Jayadeep Gopalakrishnan Incompressible Finite Elements via
Hybridization. Part I: The Stokes System
in Two Space Dimensions . . . . . . . . 1627--1650
Bernardo Cockburn and
Jayadeep Gopalakrishnan Incompressible Finite Elements via
Hybridization. Part II: The Stokes
System in Three Space Dimensions . . . . 1651--1672
Qiang Du and
Lili Ju Finite Volume Methods on Spheres and
Spherical Centroidal Voronoi Meshes . . 1673--1692
Chris Homescu and
Linda R. Petzold and
Radu Serban Error Estimation for Reduced-Order
Models of Dynamical Systems . . . . . . 1693--1714
Havard Berland and
Brynjulf Owren and
Bard Skaflestad B-series and Order Conditions for
Exponential Integrators . . . . . . . . 1715--1727
M. Berndt and
K. Lipnikov and
M. Shashkov and
M. F. Wheeler and
I. Yotov Superconvergence of the Velocity in
Mimetic Finite Difference Methods on
Quadrilaterals . . . . . . . . . . . . . 1728--1749
Peter Alfeld and
Larry L. Schumaker A $ C^2 $ Trivariate Macroelement Based
on the Worsey--Farin Split of a
Tetrahedron . . . . . . . . . . . . . . 1750--1765
R. Verfürth Robust A Posteriori Error Estimates for
Stationary Convection-Diffusion
Equations . . . . . . . . . . . . . . . 1766--1782
R. Verfürth Robust A Posteriori Error Estimates for
Nonstationary Convection-Diffusion
Equations . . . . . . . . . . . . . . . 1783--1802
Khamron Mekchay and
Ricardo H. Nochetto Convergence of Adaptive Finite Element
Methods for General Second Order Linear
Elliptic PDEs . . . . . . . . . . . . . 1803--1827
Samy Gallego and
Florian Méhats Entropic Discretization of a Quantum
Drift-Diffusion Model . . . . . . . . . 1828--1849
Heng-Bin An On Convergence of the Additive Schwarz
Preconditioned Inexact Newton Method . . 1850--1871
Franco Brezzi and
Konstantin Lipnikov and
Mikhail Shashkov Convergence of the Mimetic Finite
Difference Method for Diffusion Problems
on Polyhedral Meshes . . . . . . . . . . 1872--1896
Inga Parts and
Arvet Pedas and
Enn Tamme Piecewise Polynomial Collocation for
Fredholm Integro-Differential Equations
with Weakly Singular Kernels . . . . . . 1897--1911
Q.-Y. Chen and
D. Gottlieb and
J. S. Hesthaven Spectral Methods Based on Prolate
Spheroidal Wave Functions for Hyperbolic
PDEs . . . . . . . . . . . . . . . . . . 1912--1933
Hermann Brunner and
Qiya Hu Optimal Superconvergence Orders of
Iterated Collocation Solutions for
Volterra Integral Equations with
Vanishing Delays . . . . . . . . . . . . 1934--1949
Harbir Lamba The Effective Stability of Adaptive
Timestepping ODE Solvers . . . . . . . . 1950--1968
David Day and
Louis Romero Roots of Polynomials Expressed in Terms
of Orthogonal Polynomials . . . . . . . 1969--1987
Marcus Calhoun-Lopez and
Max D. Gunzburger A Finite Element, Multiresolution
Viscosity Method for Hyperbolic
Conservation Laws . . . . . . . . . . . 1988--2011
Erik Burman A Unified Analysis for Conforming and
Nonconforming Stabilized Finite Element
Methods Using Interior Penalty . . . . . 2012--2033
S. Van Criekingen A Linear Algebraic Analysis of Diffusion
Synthetic Acceleration for
Three-Dimensional Transport Equations 2034--2059
Sergei Pereverzev and
Eberhard Schock On the Adaptive Selection of the
Parameter in Regularization of Ill-Posed
Problems . . . . . . . . . . . . . . . . 2060--2076
Alain Bossavit and
Francesca Rapetti A Prolongation/Restriction Operator for
Whitney Elements on Simplicial Meshes 2077--2097
Hongsen Chen Pointwise Error Estimates for Finite
Element Solutions of the Stokes Problem 1--28
F. Tone and
D. Wirosoetisno On the Long-Time Stability of the
Implicit Euler Scheme for the
Two-Dimensional Navier--Stokes Equations 29--40
Albrecht Böttcher On the Problem of Testing the Structure
of a Matrix by Displacement Operations 41--54
Eskil Hansen Convergence of Multistep Time
Discretizations of Nonlinear Dissipative
Evolution Equations . . . . . . . . . . 55--65
Herbert Egger Semi-iterative Regularization in Hilbert
Scales . . . . . . . . . . . . . . . . . 66--81
Pavel B. Bochev and
Clark R. Dohrmann and
Max D. Gunzburger Stabilization of Low-order Mixed Finite
Elements for the Stokes Equations . . . 82--101
Qiang Du and
Maria Emelianenko and
Lili Ju Convergence of the Lloyd Algorithm for
Computing Centroidal Voronoi
Tessellations . . . . . . . . . . . . . 102--119
Thomas A. Manteuffel and
Stephen F. McCormick and
Oliver Röhrle and
John Ruge Projection Multilevel Methods for
Quasilinear Elliptic Partial
Differential Equations: Numerical
Results . . . . . . . . . . . . . . . . 120--138
Thomas A. Manteuffel and
Stephen F. McCormick and
Oliver Röhrle Projection Multilevel Methods for
Quasilinear Elliptic Partial
Differential Equations: Theoretical
Results . . . . . . . . . . . . . . . . 139--152
Martin Burger and
Barbara Kaltenbacher Regularizing Newton--Kaczmarz Methods
for Nonlinear Ill-Posed Problems . . . . 153--182
Xiu Ye A Discontinuous Finite Volume Method for
the Stokes Problems . . . . . . . . . . 183--198
Susanne C. Brenner and
Li-yeng Sung Multigrid Algorithms for C0 Interior
Penalty Methods . . . . . . . . . . . . 199--223
Hermann Brunner and
Dominik Schötzau hp-Discontinuous Galerkin Time-Stepping
for Volterra Integrodifferential
Equations . . . . . . . . . . . . . . . 224--245
Benqi Guo Approximation Theory for the $p$-Version
of the Finite Element Method in Three
Dimensions. Part 1: Approximabilities of
Singular Functions in the Framework of
the Jacobi-Weighted Besov and Sobolev
Spaces . . . . . . . . . . . . . . . . . 246--269
C. R. Dohrmann and
R. B. Lehoucq A Primal-Based Penalty Preconditioner
for Elliptic Saddle Point Systems . . . 270--282
N. Dokeva and
M. Dryja and
W. Proskurowski A FETI-DP Preconditioner with a Special
Scaling for Mortar Discretization of
Elliptic Problems with Discontinuous
Coefficients . . . . . . . . . . . . . . 283--299
Carlos Parés Numerical methods for nonconservative
hyperbolic systems: a theoretical
framework . . . . . . . . . . . . . . . 300--321
Rodolfo Araya and
Gabriel R. Barrenechea and
Frédéric Valentin Stabilized Finite Element Methods Based
on Multiscale Enrichment for the Stokes
Problem . . . . . . . . . . . . . . . . 322--348
K. Chrysafinos and
Noel J. Walkington Error Estimates for the Discontinuous
Galerkin Methods for Parabolic Equations 349--366
Valery Agoshkov and
Alfio Quarteroni and
Gianluigi Rozza Shape Design in Aorto-Coronaric Bypass
Anastomoses Using Perturbation Theory 367--384
Gottlieb Pirsic and
Josef Dick and
Friedrich Pillichshammer Cyclic Digital Nets, Hyperplane Nets,
and Multivariate Integration in Sobolev
Spaces . . . . . . . . . . . . . . . . . 385--411
Mihaela Negreanu and
Enrique Zuazua Discrete Ingham Inequalities and
Applications . . . . . . . . . . . . . . 412--448
L. Badea Convergence Rate of a Schwarz Multilevel
Method for the Constrained Minimization
of Nonquadratic Functionals . . . . . . 449--477
Joseph E. Pasciak and
Yanqiu Wang A Multigrid Preconditioner for the Mixed
Formulation of Linear Plane Elasticity 478--493
Alan Demlow Localized pointwise a posteriori error
estimates for gradients of piecewise
linear finite element approximations to
second-order quasilinear elliptic
problems . . . . . . . . . . . . . . . . 494--514
Do Wan Kim and
Wing Kam Liu Maximum principle and convergence
analysis for the meshfree point
collocation method . . . . . . . . . . . 515--539
Travis M. Austin and
Thomas A. Manteuffel A Least-Squares Finite Element Method
for the Linear Boltzmann Equation with
Anisotropic Scattering . . . . . . . . . 540--560
Shujuan Lü and
Qishao Lu Fourier Spectral Approximation to
Long-time Behavior of Dissipative
Generalized KdV--Burgers Equations . . . 561--585
Oksana Korostyshevskaya and
Susan E. Minkoff A Matrix Analysis of Operator-Based
Upscaling for the Wave Equation . . . . 586--612
L. Lopez and
V. Simoncini Analysis of Projection Methods for
Rational Function Approximation to the
Matrix Exponential . . . . . . . . . . . 613--635
Adel Blouza and
Frédéric Hecht and
Hervé Le Dret Two Finite Element Approximations of
Naghdi's Shell Model in Cartesian
Coordinates . . . . . . . . . . . . . . 636--654
A. K. B. Chand and
G. P. Kapoor Generalized Cubic Spline Fractal
Interpolation Functions . . . . . . . . 655--676
Matthias Geissert Discrete Maximal $ L_p $ Regularity for
Finite Element Operators . . . . . . . . 677--698
Martin J. Gander Optimized Schwarz Methods . . . . . . . 699--731
Huo-yuan Duan and
Ping Lin and
P. Saikrishnan and
Roger C. E. Tan L2-Projected Least-Squares Finite
Element Methods for the Stokes Equations 732--752
A. Ern and
J. L. Guermond Discontinuous Galerkin Methods for
Friedrichs' Systems. I. General theory 753--778
Evelyn Buckwar and
Renate Winkler Multistep methods for SDEs and their
application to problems with small noise 779--803
Amiya K. Pani and
Jin Yun Yuan and
Pedro D. Damázio On a Linearized Backward Euler Method
for the Equations of Motion of Oldroyd
Fluids of Order One . . . . . . . . . . 804--825
Christine Bernardi and
Nejmeddine Chorfi Spectral Discretization of the
Vorticity, Velocity, and Pressure
Formulation of the Stokes Problem . . . 826--850
Mechthild Thalhammer A fourth-order commutator-free
exponential integrator for nonautonomous
differential equations . . . . . . . . . 851--864
Radu Alexandru Todor Robust Eigenvalue Computation for
Smoothing Operators . . . . . . . . . . 865--878
Adam M. Oberman Convergent Difference Schemes for
Degenerate Elliptic and Parabolic
Equations: Hamilton--Jacobi Equations
and Free Boundary Problems . . . . . . . 879--895
Greg Kuperberg Numerical Cubature Using
Error-Correcting Codes . . . . . . . . . 897--907
Greg Kuperberg Numerical Cubature from Archimedes'
Hat-box Theorem . . . . . . . . . . . . 908--935
Thomas Pok-Yin Yu How Data Dependent is a Nonlinear
Subdivision Scheme? A Case Study Based
on Convexity Preserving Subdivision . . 936--948
Serge Nicaise A Posteriori Error Estimations of Some
Cell Centered Finite Volume Methods for
Diffusion-Convection-Reaction Problems 949--978
Daniele Boffi and
Martin Costabel and
Monique Dauge and
Leszek Demkowicz Discrete Compactness for the hp Version
of Rectangular Edge Finite Elements . . 979--1004
Burak Aksoylu and
Michael Holst Optimality of Multilevel Preconditioners
for Local Mesh Refinement in Three
Dimensions . . . . . . . . . . . . . . . 1005--1025
Daan Huybrechs and
Stefan Vandewalle On the Evaluation of Highly Oscillatory
Integrals by Analytic Continuation . . . 1026--1048
Xiaobing Feng Fully Discrete Finite Element
Approximations of the
Navier--Stokes--Cahn--Hilliard Diffuse
Interface Model for Two-Phase Fluid
Flows . . . . . . . . . . . . . . . . . 1049--1072
Thomas Strohmer and
Jared Tanner Fast Reconstruction Methods for
Bandlimited Functions from Periodic
Nonuniform Sampling . . . . . . . . . . 1073--1094
Tom Lyche and
Jean-Louis Merrien C1 Interpolatory Subdivision with Shape
Constraints for Curves . . . . . . . . . 1095--1121
Graeme Fairweather and
Qun Lin and
Yanping Lin and
Junping Wang and
Shuhua Zhang Asymptotic Expansions and Richardson
Extrapolation of Approximate Solutions
for Second Order Elliptic Problems on
Rectangular Domains by Mixed Finite
Element Methods . . . . . . . . . . . . 1122--1149
Todd Arbogast and
Kirsten J. Boyd Subgrid Upscaling and Mixed Multiscale
Finite Elements . . . . . . . . . . . . 1150--1171
Lars Diening and
Andreas Prohl and
Michael R\ocircu\vzi\vcka Semi-implicit Euler Scheme for
Generalized Newtonian Fluids . . . . . . 1172--1190
E. Bécache and
A. S. Bonnet-Ben Dhia and
G. Legendre Perfectly Matched Layers for
Time-Harmonic Acoustics in the Presence
of a Uniform Flow . . . . . . . . . . . 1191--1217
John W. Barrett and
Robert Nürnberg and
Mark R. E. Warner Finite Element Approximation of Soluble
Surfactant Spreading on a Thin Film . . 1218--1247
Erik Burman and
Miguel A. Fernández and
Peter Hansbo Continuous Interior Penalty Finite
Element Method for Oseen's Equations . . 1248--1274
Chris Siefert and
Eric de Sturler Preconditioners for Generalized
Saddle-Point Problems . . . . . . . . . 1275--1296
Selim Esedoglu Stability Properties of the
Perona--Malik Scheme . . . . . . . . . . 1297--1313
M. Ganesh and
H. N. Mhaskar Matrix-free Interpolation on the Sphere 1314--1331
María López-Fernández and
César Palencia and
Achim Schädle A Spectral Order Method for Inverting
Sectorial Laplace Transforms . . . . . . 1332--1350
M. C. De Bonis and
G. Mastroianni Projection Methods and Condition Numbers
in Uniform Norm for Fredholm and Cauchy
Singular Integral Equations . . . . . . 1351--1374
Clint Dawson Analysis of Discontinuous Finite Element
Methods for Ground Water/Surface Water
Coupling . . . . . . . . . . . . . . . . 1375--1404
Sören Bartels and
Andreas Prohl Convergence of an Implicit Finite
Element Method for the
Landau--Lifshitz--Gilbert Equation . . . 1405--1419
A. Buffa and
T. J. R. Hughes and
G. Sangalli Analysis of a Multiscale Discontinuous
Galerkin Method for Convection-Diffusion
Problems . . . . . . . . . . . . . . . . 1420--1440
J. P. Coleman and
L. Gr. Ixaru Truncation Errors in Exponential Fitting
for Oscillatory Problems . . . . . . . . 1441--1465
Jinwoo Lee and
Dongwoo Sheen A Parallel Method for Backward Parabolic
Problems Based on the Laplace
Transformation . . . . . . . . . . . . . 1466--1486
Ivan G. Graham and
William McLean Anisotropic Mesh Refinement: The
Conditioning of Galerkin Boundary
Element Matrices and Simple
Preconditioners . . . . . . . . . . . . 1487--1513
Hyea Hyun Kim and
Olof B. Widlund Two-Level Schwarz Algorithms with
Overlapping Subregions for Mortar Finite
Elements . . . . . . . . . . . . . . . . 1514--1534
Stefania Bellavia and
Benedetta Morini Subspace Trust-Region Methods for Large
Bound-Constrained Nonlinear Equations 1535--1555
M. Luká\vcová-Medvi ová and
G. Warnecke and
Y. Zahaykah On the Stability of Evolution Galerkin
Schemes Applied to a Two-Dimensional
Wave Equation System . . . . . . . . . . 1556--1583
Han-Sheng Shi and
Hong-Lin Liao Unconditional Stability of Corrected
Explicit-Implicit Domain Decomposition
Algorithms for Parallel Approximation of
Heat Equations . . . . . . . . . . . . . 1584--1611
Erik Burman and
Paolo Zunino A Domain Decomposition Method Based on
Weighted Interior Penalties for
Advection-Diffusion-Reaction Problems 1612--1638
Songul Kaya and
William Layton and
Béatrice Rivi\`ere Subgrid Stabilized Defect Correction
Methods for the Navier--Stokes Equations 1639--1654
Helge Holden and
Xavier Raynaud Convergence of a Finite Difference
Scheme for the Camassa--Holm Equation 1655--1680
Yubin Yan Postprocessing the Finite Element Method
for Semilinear Parabolic Problems . . . 1681--1702
Qiang Zhang and
Chi-Wang Shu Error Estimates to Smooth Solutions of
Runge--Kutta Discontinuous Galerkin
Method for Symmetrizable Systems of
Conservation Laws . . . . . . . . . . . 1703--1720
Zhiqiang Cai and
Jaeun Ku The $ {L}^2 $ Norm Error Estimates for
the Div Least-Squares Method . . . . . . 1721--1734
Inmaculada Higueras Strong Stability for Additive
Runge--Kutta Methods . . . . . . . . . . 1735--1758
Chuanju Xu and
Tao Tang Stability Analysis of Large
Time-Stepping Methods for Epitaxial
Growth Models . . . . . . . . . . . . . 1759--1779
Leevan Ling Finding Numerical Derivatives for
Unstructured and Noisy Data by
Multiscale Kernels . . . . . . . . . . . 1780--1800
Shi Jin and
Xin Wen A Hamiltonian-Preserving Scheme for the
Liouville Equation of Geometrical Optics
with Partial Transmissions and
Reflections . . . . . . . . . . . . . . 1801--1828
Alfredo Bermúdez and
Maria R. Nogueiras and
Carlos Vázquez Numerical Analysis of
Convection-Diffusion-Reaction Problems
with Higher Order Characteristics/Finite
Elements. Part I: Time Discretization 1829--1853
Alfredo Bermúdez and
Maria R. Nogueiras and
Carlos Vázquez Numerical Analysis of
Convection-Diffusion-Reaction Problems
with Higher Order Characteristics/Finite
Elements. Part II: Fully Discretized
Scheme and Quadrature Formulas . . . . . 1854--1876
Kit Hung Chan and
Keke Zhang and
Jun Zou Spherical Interface Dynamos:
Mathematical Theory, Finite Element
Approximation, and Application . . . . . 1877--1902
Arnd Rösch and
Boris Vexler Optimal Control of the Stokes Equations:
A Priori Error Analysis for Finite
Element Discretization with
Postprocessing . . . . . . . . . . . . . 1903--1920
Katarina Jegdic and
Robert L. Jerrard Convergence of an Implicit Spacetime
Godunov Finite Volume Method for a Class
of Hyperbolic Systems . . . . . . . . . 1921--1953
Francesca Mazzia and
Alessandra Sestini and
Donato Trigiante B-Spline Linear Multistep Methods and
their Continuous Extensions . . . . . . 1954--1973
E. Lee and
T. A. Manteuffel and
C. R. Westphal Weighted-Norm First-Order System Least
Squares (FOSLS) for Problems with Corner
Singularities . . . . . . . . . . . . . 1974--1996
Matania Ben-Artzi and
Jean-Pierre Croisille and
Dalia Fishelov Convergence of a Compact Scheme for the
Pure Streamfunction Formulation of the
Unsteady Navier--Stokes System . . . . . 1997--2024
S. Manservisi Numerical Analysis of Vanka-Type Solvers
for Steady Stokes and Navier--Stokes
Flows . . . . . . . . . . . . . . . . . 2025--2056
T. A. Manteuffel and
S. F. McCormick and
J. G. Schmidt and
C. R. Westphal First-Order System Least Squares for
Geometrically Nonlinear Elasticity . . . 2057--2081
Mary F. Wheeler and
Ivan Yotov A Multipoint Flux Mixed Finite Element
Method . . . . . . . . . . . . . . . . . 2082--2106
R. Hiptmair and
P. Meury Stabilized FEM-BEM Coupling for
Helmholtz Transmission Problems . . . . 2107--2130
Eric T. Chung and
Björn Engquist Optimal Discontinuous Galerkin Methods
for Wave Propagation . . . . . . . . . . 2131--2158
Santiago Badia and
Ramon Codina Analysis of a Stabilized Finite Element
Approximation of the Transient
Convection-Diffusion Equation Using an
ALE Framework . . . . . . . . . . . . . 2159--2197
Annalisa Buffa and
Ilaria Perugia Discontinuous Galerkin Approximation of
the Maxwell Eigenproblem . . . . . . . . 2198--2226
Lidia Aceto and
Paolo Ghelardoni and
Giovanni Gheri An Algebraic Procedure for the Spectral
Corrections Using the Miss-Distance
Functions in Regular and Singular
Sturm--Liouville Problems . . . . . . . 2227--2243
Jean-Baptiste Apoung Kamga and
Bruno Després CFL Condition and Boundary Conditions
for DGM Approximation of
Convection-Diffusion . . . . . . . . . . 2245--2269
Markos A. Katsoulakis and
Petr Plechá and
Alexandros Sopasakis Error Analysis of Coarse-Graining for
Stochastic Lattice Dynamics . . . . . . 2270--2296
Fatih Celiker and
Bernardo Cockburn and
Henryk K. Stolarski Locking-Free Optimal Discontinuous
Galerkin Methods for Timoshenko Beams 2297--2325
Xiaojun Chen and
Robert S. Womersley Existence of Solutions to Systems of
Underdetermined Equations and Spherical
Designs . . . . . . . . . . . . . . . . 2326--2341
J. A. C. Weideman and
L. N. Trefethen Optimizing Talbot's Contours for the
Inversion of the Laplace Transform . . . 2342--2362
Alexandre Ern and
Jean-Luc Guermond Discontinuous Galerkin Methods for
Friedrichs' Systems. Part II.
Second-order Elliptic PDEs . . . . . . . 2363--2388
Jörg Peters and
Xiaobin Wu On the Local Linear Independence of
Generalized Subdivision Functions . . . 2389--2407
Marcus J. Grote and
Anna Schneebeli and
Dominik Schötzau Discontinuous Galerkin Finite Element
Method for the Wave Equation . . . . . . 2408--2431
Jing Li and
Olof Widlund BDDC Algorithms for Incompressible
Stokes Equations . . . . . . . . . . . . 2432--2455
Jian-Guo Liu and
Wei-Cheng Wang Convergence Analysis of the Energy and
Helicity Preserving Scheme for
Axisymmetric Flows . . . . . . . . . . . 2456--2480
Michael Eiermann and
Oliver G. Ernst A Restarted Krylov Subspace Method for
the Evaluation of Matrix Functions . . . 2481--2504
Emmanuel Gobet and
Gilles Pag\`es and
Huyên Pham and
Jacques Printems Discretization and Simulation of the
Zakai Equation . . . . . . . . . . . . . 2505--2538
Lizhen Qin and
Xuejun Xu On a Parallel Robin-Type Nonoverlapping
Domain Decomposition Method . . . . . . 2539--2558
Rong-Xian Yue and
Fred J. Hickernell Strong Tractability of Quasi-Monte Carlo
Quadrature Using Nets for Certain Banach
Spaces . . . . . . . . . . . . . . . . . 2559--2583
J. C. Jimenez and
L. M. Pedroso and
F. Carbonell and
V. Hernandez Local Linearization Method for Numerical
Integration of Delay Differential
Equations . . . . . . . . . . . . . . . 2584--2609
Stéphane Menozzi Improved Simulation for the Killed
Brownian Motion in a Cone . . . . . . . 2610--2632
Constantin Bacuta A Unified Approach for Uzawa Algorithms 2633--2649
Béatrice Rivi\`ere and
Simon Shaw Discontinuous Galerkin Finite Element
Approximation of Nonlinear Non-Fickian
Diffusion in Viscoelastic Polymers . . . 2650--2670
K. G. Van Der Zee and
E. H. Van Brummelen and
R. De Borst An $ H^1 (\mathcal {P}^{\mathsf {h}})
$-Coercive Discontinuous Galerkin
Formulation for the Poisson Problem:
$1$D Analysis . . . . . . . . . . . . . 2671--2698
R. Eymard and
R. Herbin and
J. C. Latché Convergence Analysis of a Colocated
Finite Volume Scheme for the
Incompressible Navier--Stokes Equations
on General $2$D or $3$D Meshes . . . . . 1--36
L. Banjai and
S. Sauter A Refined Galerkin Error and Stability
Analysis for Highly Indefinite
Variational Problems . . . . . . . . . . 37--53
Sergej Rjasanow and
Wolfgang Wagner Time Splitting Error in DSMC Schemes for
the Spatially Homogeneous Inelastic
Boltzmann Equation . . . . . . . . . . . 54--67
Carsten Carstensen and
Jun Hu and
Antonio Orlando Framework for the A Posteriori Error
Analysis of Nonconforming Finite
Elements . . . . . . . . . . . . . . . . 68--82
Jianliang Qian and
Yong-Tao Zhang and
Hong-Kai Zhao Fast Sweeping Methods for Eikonal
Equations on Triangular Meshes . . . . . 83--107
Yuan Xu and
Oleg Tischenko and
Christoph Hoeschen Approximation and Reconstruction from
Attenuated Radon Projections . . . . . . 108--132
Rob Stevenson Composite Wavelet Bases with Extended
Stability and Cancellation Properties 133--162
Thirupathi Gudi and
Amiya K. Pani Discontinuous Galerkin Methods for
Quasi-Linear Elliptic Problems of
Nonmonotone Type . . . . . . . . . . . . 163--192
Mark A. Taylor and
Beth A. Wingate and
Len P. Bos A Cardinal Function Algorithm for
Computing Multivariate Quadrature Points 193--205
Jan Maes and
Angela Kunoth and
Adhemar Bultheel BPX-type Preconditioners for Second and
Fourth Order Elliptic Problems on the
Sphere . . . . . . . . . . . . . . . . . 206--222
Thomas F. Russell and
Mary F. Wheeler and
Ivan Yotov Superconvergence for Control-Volume
Mixed Finite Element Methods on
Rectangular Grids . . . . . . . . . . . 223--235
M. Neher and
K. R. Jackson and
N. S. Nedialkov On Taylor Model Based Integration of
ODEs . . . . . . . . . . . . . . . . . . 236--262
K. I. Dickson and
C. T. Kelley and
I. C. F. Ipsen and
I. G. Kevrekidis Condition Estimates for Pseudo-Arclength
Continuation . . . . . . . . . . . . . . 263--276
Gabriel Acosta and
María G. Armentano and
Ricardo G. Durán and
Ariel L. Lombardi Finite Element Approximations in a
NonLipschitz Domain . . . . . . . . . . 277--295
Fang Liu and
Aihui Zhou Two-Scale Boolean Galerkin
Discretizations for Fredholm Integral
Equations of the Second Kind . . . . . . 296--312
Ping Lin Convergence Analysis of a
Quasi-Continuum Approximation for a
Two-Dimensional Material Without Defects 313--332
Robert Schaback Convergence of Unsymmetric Kernel-Based
Meshless Collocation Methods . . . . . . 333--351
Jun Shen and
Chi-Wang Shu and
Mengping Zhang High Resolution Schemes for a
Hierarchical Size-Structured Model . . . 352--370
Gerhard Starke An Adaptive Least-Squares Mixed Finite
Element Method for Elasto-Plasticity . . 371--388
Juan E. Santos and
Dongwoo Sheen Finite Element Methods for the
Simulation of Waves in Composite
Saturated Poroviscoelastic Media . . . . 389--420
Alan Demlow and
Gerhard Dziuk An Adaptive Finite Element Method for
the Laplace--Beltrami Operator on
Implicitly Defined Surfaces . . . . . . 421--442
Givi Berikelashvili and
Murli M. Gupta and
Manana Mirianashvili Convergence of Fourth Order Compact
Difference Schemes for Three-Dimensional
Convection-Diffusion Equations . . . . . 443--455
Lars Diening and
Carsten Ebmeyer and
Michael R\ocircu\vzi\vcka Optimal Convergence for the Implicit
Space--time Discretization of Parabolic
Systems with $p$-Structure . . . . . . . 457--472
Amin Boumenir and
Vu Kim Tuan Sampling Eigenvalues in Hardy Spaces . . 473--483
Juergen Rodenkirchen Maximum $ L^2 $-Convergence Rates of the
Crank--Nicolson Scheme to the Stokes
Initial Value Problem . . . . . . . . . 484--499
Zden k Dostál and
David Horák Theoretically Supported Scalable FETI
for Numerical Solution of Variational
Inequalities . . . . . . . . . . . . . . 500--513
Andreas Dedner and
Charalambos Makridakis and
Mario Ohlberger Error Control for a Class of
Runge--Kutta Discontinuous Galerkin
Methods for Nonlinear Conservation Laws 514--538
T. J. R. Hughes and
G. Sangalli Variational Multiscale Analysis: the
Fine-scale Green's Function, Projection,
Optimization, Localization, and
Stabilized Methods . . . . . . . . . . . 539--557
Thomas Schmelzer and
Lloyd N. Trefethen Computing the Gamma Function Using
Contour Integrals and Rational
Approximations . . . . . . . . . . . . . 558--571
Vincent J. Ervin and
Norbert Heuer and
John Paul Roop Numerical Approximation of a Time
Dependent, Nonlinear, Space-Fractional
Diffusion Equation . . . . . . . . . . . 572--591
Desmond J. Higham and
Xuerong Mao and
Chenggui Yuan Almost Sure and Moment Exponential
Stability in the Numerical Simulation of
Stochastic Differential Equations . . . 592--609
S. N. Chandler-Wilde and
S. Langdon A Galerkin Boundary Element Method for
High Frequency Scattering by Convex
Polygons . . . . . . . . . . . . . . . . 610--640
Ohannes A. Karakashian and
Frederic Pascal Convergence of Adaptive Discontinuous
Galerkin Approximations of Second-Order
Elliptic Problems . . . . . . . . . . . 641--665
M. J. Gander and
L. Halpern Optimized Schwarz Waveform Relaxation
Methods for Advection Reaction Diffusion
Problems . . . . . . . . . . . . . . . . 666--697
Benqi Guo and
Weiwei Sun The Optimal Convergence of the $h$-$p$
Version of the Finite Element Method
with Quasi-Uniform Meshes . . . . . . . 698--730
Garvin Danisch and
Gerhard Starke First-Order System Least-Squares for
Darcy--Stokes Flow . . . . . . . . . . . 731--745
Bernhard Beckermann and
Stefano Serra-Capizzano On the Asymptotic Spectrum of Finite
Element Matrix Sequences . . . . . . . . 746--769
B. de la Calle Ysern and
F. Peherstorfer Ultraspherical Stieltjes Polynomials and
Gauss--Kronrod Quadrature Behave Nicely
for $ \lambda < 0 $ . . . . . . . . . . . 770--786
Eunjung Lee and
Thomas A. Manteuffel FOSLL* Method for the Eddy Current
Problem with Three-Dimensional Edge
Singularities . . . . . . . . . . . . . 787--809
Florian Frühauf and
Bastian Gebauer and
Otmar Scherzer Detecting Interfaces in a
Parabolic-Elliptic Problem from Surface
Measurements . . . . . . . . . . . . . . 810--836
Yinnian He and
Weiwei Sun Stability and Convergence of the
Crank--Nicolson/Adams--Bashforth scheme
for the Time-Dependent Navier--Stokes
Equations . . . . . . . . . . . . . . . 837--869
Gabriel J. Lord and
Tony Shardlow Postprocessing for Stochastic Parabolic
Partial Differential Equations . . . . . 870--889
K. Avrachenkov and
N. Litvak and
D. Nemirovsky and
N. Osipova Monte Carlo Methods in PageRank
Computation: When One Iteration is
Sufficient . . . . . . . . . . . . . . . 890--904
John W. Barrett and
Sören Bartels and
Xiaobing Feng and
Andreas Prohl A Convergent and Constraint-Preserving
Finite Element Method for the
$p$-Harmonic Flow into Spheres . . . . . 905--927
Sergey Repin and
Stefan Sauter and
Anton Smolianski Two-Sided A Posteriori Error Estimates
for Mixed Formulations of Elliptic
Problems . . . . . . . . . . . . . . . . 928--945
Isabelle Greff Nonconforming Box-Schemes for Elliptic
Problems on Rectangular Grids . . . . . 946--968
S. González-Pinto and
D. Hernández-Abreu On the Contractivity and Convergence of
General Linear Methods on Semi-Infinite
Intervals . . . . . . . . . . . . . . . 969--985
Hermann Brunner and
Qiya Hu Optimal Superconvergence Results for
Delay Integro-Differential Equations of
Pantograph Type . . . . . . . . . . . . 986--1004
Ivo Babu\vska and
Fabio Nobile and
Raúl Tempone A Stochastic Collocation Method for
Elliptic Partial Differential Equations
with Random Input Data . . . . . . . . . 1005--1034
Yvan Notay Convergence Analysis of Perturbed
Two-Grid and Multigrid Methods . . . . . 1035--1044
Kou-Kung Alex Chang The Stability of Front-Tracking Scheme
for Two Spatial Dimensional Miscible Two
Phase Flow . . . . . . . . . . . . . . . 1045--1063
Jeffrey S. Ovall Function, Gradient, and Hessian Recovery
Using Quadratic Edge-Bump Functions . . 1064--1080
C. V. Pao Numerical Methods for Quasi-Linear
Elliptic Equations with Nonlinear
Boundary Conditions . . . . . . . . . . 1081--1106
Jürgen Hartinger and
Volker Ziegler On Corner Avoidance Properties of
Random-Start Halton Sequences . . . . . 1109--1121
Bernd Hofmann and
Peter Mathé Analysis of Profile Functions for
General Linear Regularization Methods 1122--1141
Sarah Delcourte and
Komla Domelevo and
Pascal Omnes A Discrete Duality Finite Volume
Approach to Hodge Decomposition and
div-curl Problems on Almost Arbitrary
Two-Dimensional Meshes . . . . . . . . . 1142--1174
Markus Holtz and
Angela Kunoth B-Spline-Based Monotone Multigrid
Methods . . . . . . . . . . . . . . . . 1175--1199
Gang Xie and
Thomas P.-Y. Yu Smoothness Equivalence Properties of
Manifold-Valued Data Subdivision Schemes
Based on the Projection Approach . . . . 1200--1225
M. N. Spijker Stepsize Conditions for General
Monotonicity in Numerical Initial Value
Problems . . . . . . . . . . . . . . . . 1226--1245
Marco Discacciati and
Alfio Quarteroni and
Alberto Valli Robin--Robin Domain Decomposition
Methods for the Stokes--Darcy Coupling 1246--1268
Junping Wang and
Xiu Ye New Finite Element Methods in
Computational Fluid Dynamics by H(div)
Elements . . . . . . . . . . . . . . . . 1269--1286
Chun Liu and
Noel J. Walkington Convergence of Numerical Approximations
of the Incompressible Navier--Stokes
Equations with Variable Density and
Viscosity . . . . . . . . . . . . . . . 1287--1304
Hong Wang and
Kaixin Wang Uniform Estimates for
Eulerian--Lagrangian Methods for
Singularly Perturbed Time-Dependent
Problems . . . . . . . . . . . . . . . . 1305--1329
Xudong Yao and
Jianxin Zhou Unified Convergence Results on a Minimax
Algorithm for Finding Multiple Critical
Points in Banach Spaces . . . . . . . . 1330--1347
Jaap J. W. van der Vegt and
Ferenc Izsák and
Onno Bokhove Error Analysis of a
Continuous-Discontinuous Galerkin Finite
Element Method for Generalized $2$D
Vorticity Dynamics . . . . . . . . . . . 1349--1369
Christoph Ortner and
Endre Süli Discontinuous Galerkin Finite Element
Approximation of Nonlinear Second-Order
Elliptic and Hyperbolic Systems . . . . 1370--1397
Sarah Day and
Jean-Philippe Lessard and
Konstantin Mischaikow Validated Continuation for Equilibria of
PDEs . . . . . . . . . . . . . . . . . . 1398--1424
Hongyun Wang Convergence of a Numerical Method for
Solving Discontinuous Fokker--Planck
Equations . . . . . . . . . . . . . . . 1425--1452
Huazhong Tang and
Gerald Warnecke On Convergence of a Domain Decomposition
Method for a Scalar Conservation Law . . 1453--1471
Mario Bebendorf Why Finite Element Discretizations Can
Be Factored by Triangular Hierarchical
Matrices . . . . . . . . . . . . . . . . 1472--1494
Owe Axelsson and
János Karátson Mesh Independent Superlinear PCG Rates
Via Compact-Equivalent Operators . . . . 1495--1516
Paul Deuring A Finite Element Method for $3$D
Exterior Oseen Flows: Error Estimates 1517--1543
Andris Lasis and
Endre Süli $ h p$-Version Discontinuous Galerkin
Finite Element Method for Semilinear
Parabolic Problems . . . . . . . . . . . 1544--1569
Martin Vohralík A Posteriori Error Estimates for
Lowest-Order Mixed Finite Element
Discretizations of
Convection-Diffusion-Reaction Equations 1570--1599
Sebastiano Boscarino Error Analysis of IMEX Runge--Kutta
Methods Derived from
Differential-Algebraic Systems . . . . . 1600--1621
Leo G. Rebholz An Energy- and Helicity-Conserving
Finite Element Scheme for the
Navier--Stokes Equations . . . . . . . . 1622--1638
So-Hsiang Chou and
Xiu Ye Unified Analysis of Finite Volume
Methods for Second Order Elliptic
Problems . . . . . . . . . . . . . . . . 1639--1653
Andrea Cangiani and
Endre Süli The Residual-Free-Bubble Finite Element
Method on Anisotropic Partitions . . . . 1654--1678
Sven Gross and
Arnold Reusken Finite Element Discretization Error
Analysis of a Surface Tension Force in
Two-Phase Incompressible Flows . . . . . 1679--1700
Haijun Wu and
Zhimin Zhang Can We Have Superconvergent Gradient
Recovery Under Adaptive Meshes? . . . . 1701--1722
Peter Giesl and
Holger Wendland Meshless Collocation: Error Estimates
with Application to Dynamical Systems 1723--1741
Bernardo Cockburn and
Jayadeep Gopalakrishnan and
Haiying Wang Locally Conservative Fluxes for the
Continuous Galerkin Method . . . . . . . 1742--1776
Mark Ainsworth A Posteriori Error Estimation for
Discontinuous Galerkin Finite Element
Approximation . . . . . . . . . . . . . 1777--1798
Borislav Bojanov and
Yuan Xu Erratum: On a Hermite interpolation by
polynomials of two variables . . . . . . 1799--1800
Mo Mu and
Jinchao Xu A Two-Grid Method of a Mixed
Stokes--Darcy Model for Coupling Fluid
Flow with Porous Media Flow . . . . . . 1801--1813
Laurent O. Jay Specialized Partitioned Additive
Runge--Kutta Methods for Systems of
Overdetermined DAEs with Holonomic
Constraints . . . . . . . . . . . . . . 1814--1842
T. Tachim Medjo A Small Eddy Correction Method for a
$3$D Navier--Stokes-Type System of
Equations Related to the Primitive
Equations of the Ocean . . . . . . . . . 1843--1870
Rong Wang and
Raymond J. Spiteri Linear Instability of the Fifth-Order
WENO Method . . . . . . . . . . . . . . 1871--1901
Stefan Nilsson and
N. Anders Petersson and
Björn Sjögreen and
Heinz-Otto Kreiss Stable Difference Approximations for the
Elastic Wave Equation in Second Order
Formulation . . . . . . . . . . . . . . 1902--1936
Klaus Deckelnick and
Michael Hinze Convergence of a Finite Element
Approximation to a State-Constrained
Elliptic Control Problem . . . . . . . . 1937--1953
Jie Shen and
Li-Lian Wang Analysis of a Spectral-Galerkin
Approximation to the Helmholtz Equation
in Exterior Domains . . . . . . . . . . 1954--1978
Emiliano Cristiani and
Maurizio Falcone Fast Semi-Lagrangian Schemes for the
Eikonal Equation and Applications . . . 1979--2011
Patrick Hild and
Yves Renard An Error Estimate for the Signorini
Problem with Coulomb Friction
Approximated by Finite Elements . . . . 2012--2031
Randolph E. Bank and
Jinchao Xu and
Bin Zheng Superconvergent Derivative Recovery for
Lagrange Triangular Elements of Degree
$p$ on Unstructured Grids . . . . . . . 2032--2046
L. Beirão da Veiga and
J. Niiranen and
R. Stenberg A Family of $ {C}^0 $ Finite Elements
For Kirchhoff Plates I: Error Analysis 2047--2071
Gabriel N. Gatica and
Antonio Márquez and
Salim Meddahi Analysis of the Coupling of Primal and
Dual-Mixed Finite Element Methods for a
Two-Dimensional Fluid-Solid Interaction
Problem . . . . . . . . . . . . . . . . 2072--2097
Fausto Cavalli and
Giovanni Naldi and
Gabriella Puppo and
Matteo Semplice High-Order Relaxation Schemes for
Nonlinear Degenerate Diffusion Problems 2098--2119
Vincent J. Ervin and
Hyesuk Lee Numerical Approximation of a
Quasi-Newtonian Stokes Flow Problem with
Defective Boundary Conditions . . . . . 2120--2140
Josef Dick Explicit Constructions of Quasi-Monte
Carlo Rules for the Numerical
Integration of High-Dimensional Periodic
Functions . . . . . . . . . . . . . . . 2141--2176
Weizhu Bao and
Hanquan Wang A Mass and Magnetization Conservative
and Energy-Diminishing Numerical Method
for Computing Ground State of Spin-1
Bose--Einstein Condensates . . . . . . . 2177--2200
Benjamin Hackl Methods for Reliable Topology Changes
for Perimeter-Regularized Geometric
Inverse Problems . . . . . . . . . . . . 2201--2227
Claire Chainais-Hillairet and
Jérôme Droniou Convergence Analysis of a Mixed Finite
Volume Scheme for an Elliptic-Parabolic
System Modeling Miscible Fluid Flows in
Porous Media . . . . . . . . . . . . . . 2228--2258
Philippe Poncet Analysis of Direct Three-Dimensional
Parabolic Panel Methods . . . . . . . . 2259--2297
Long Chen and
Michael J. Holst and
Jinchao Xu The Finite Element Approximation of the
Nonlinear Poisson--Boltzmann Equation 2298--2320
Sven Beuchler and
Sergey V. Nepomnyaschikh Overlapping Additive Schwarz
Preconditioners for Elliptic Problems
with Degenerate Locally Anisotropic
Coefficients . . . . . . . . . . . . . . 2321--2344
Daniele Bertaccini and
Fabio Di Benedetto Spectral Analysis of Nonsymmetric
Quasi-Toeplitz matrices with
Applications to Preconditioned Multistep
Formulas . . . . . . . . . . . . . . . . 2345--2367
Weiming Cao An Interpolation Error Estimate on
Anisotropic Meshes in $ \mathcal {R}^n $
and Optimal Metrics for Mesh Refinement 2368--2391
Leopoldo P. Franca and
Volker John and
Gunar Matthies and
Lutz Tobiska An inf-sup Stable and Residual-Free
Bubble Element for the Oseen Equations 2392--2407
Alina Chertock and
Alexander Kurganov and
Yurii Rykov A New Sticky Particle Method for
Pressureless Gas Dynamics . . . . . . . 2408--2441
Yingjie Liu and
Chi-Wang Shu and
Eitan Tadmor and
Mengping Zhang Central Discontinuous Galerkin Methods
on Overlapping Cells with a
Nonoscillatory Hierarchical
Reconstruction . . . . . . . . . . . . . 2442--2467
Yvon Maday and
Julien Salomon and
Gabriel Turinici Monotonic Parareal Control for Quantum
Systems . . . . . . . . . . . . . . . . 2468--2482
Ralf Hiptmair and
Jinchao Xu Nodal Auxiliary Space Preconditioning in
H(curl) and H(div) Spaces . . . . . . . 2483--2509
Ed Bueler Error Bounds for Approximate Eigenvalues
of Periodic-Coefficient Linear Delay
Differential Equations . . . . . . . . . 2510--2536
Huo-Yuan Duan and
Ping Lin and
P. Saikrishnan and
Roger C. E. Tan A Least-Squares Finite Element Method
for the Magnetostatic Problem in a
Multiply Connected Lipschitz Domain . . 2537--2563
W. Gawronski and
J. Müller and
M. Reinhard Reduced Cancellation in the Evaluation
of Entire Functions and Applications to
the Error Function . . . . . . . . . . . 2564--2576
Donald E. Marshall and
Steffen Rohde Convergence of a Variant of the Zipper
Algorithm for Conformal Mapping . . . . 2577--2609
N. Bissantz and
T. Hohage and
A. Munk and
F. Ruymgaart Convergence Rates of General
Regularization Methods for Statistical
Inverse Problems and Applications . . . 2610--2636
M. I. M. Copetti Numerical Analysis of a Unilateral
Problem in Planar Thermoelasticity . . . 2637--2652
Christine Bernardi and
Adel Blouza Spectral Discretization of a Naghdi
Shell Model . . . . . . . . . . . . . . 2653--2670
Ralf Hartmann Adjoint Consistency Analysis of
Discontinuous Galerkin Discretizations 2671--2696
Houman Owhadi and
Lei Zhang Homogenization of Parabolic Equations
with a Continuum of Space and Time
Scales . . . . . . . . . . . . . . . . . 1--36
Olga Drblíková and
Karol Mikula Convergence Analysis of Finite Volume
Scheme for Nonlinear Tensor Anisotropic
Diffusion in Image Processing . . . . . 37--60
Sören Bartels and
Xiaobing Feng and
Andreas Prohl Finite Element Approximations of Wave
Maps into Spheres . . . . . . . . . . . 61--87
Jun Hu and
Zhong-Ci Shi Lower Order Rectangular Nonconforming
Mixed Finite Elements for Plane
Elasticity . . . . . . . . . . . . . . . 88--102
V. Gradinaru Strang Splitting for the Time-Dependent
Schrödinger Equation on Sparse Grids . . 103--123
Benoit Merlet $ L^\infty $- and $ L^2 $-Error
Estimates for a Finite Volume
Approximation of Linear Advection . . . 124--150
V. John and
W. Layton and
C. C. Manica Convergence of Time-Averaged Statistics
of Finite Element Approximations of the
Navier--Stokes Equations . . . . . . . . 151--179
Christian Jansson and
Denis Chaykin and
Christian Keil Rigorous Error Bounds for the Optimal
Value in Semidefinite Programming . . . 180--200
Javier de Frutos and
Bosco García-Archilla and
Julia Novo The Postprocessed Mixed Finite-Element
Method for the Navier--Stokes Equations:
Refined Error Bounds . . . . . . . . . . 201--230
Xu Da Uniform $ l^1 $ Behavior for Time
Discretization of a Volterra Equation
with Completely Monotonic Kernel II:
Convergence . . . . . . . . . . . . . . 231--259
Zhangxin Chen and
Tatyana Y. Savchuk Analysis of the Multiscale Finite
Element Method for Nonlinear and Random
Homogenization Problems . . . . . . . . 260--279
Marios Charalambides and
Fabian Waleffe Spectrum of the Jacobi Tau Approximation
for the Second Derivative Operator . . . 280--294
Xiaoying Dai and
Aihui Zhou Three-Scale Finite Element
Discretizations for Quantum Eigenvalue
Problems . . . . . . . . . . . . . . . . 295--324
Zheng Ran Lie Symmetry Preservation and
Shock-Capturing Methods . . . . . . . . 325--343
Amiya Kumar Pani and
Graeme Fairweather and
Ryan I. Fernandes Alternating Direction Implicit
Orthogonal Spline Collocation Methods
for an Evolution Equation with a
Positive-Type Memory Term . . . . . . . 344--364
T. Yu. Bohonova and
I. P. Gavrilyuk and
V. L. Makarov and
V. Vasylyk Exponentially Convergent Duhamel-Like
Algorithms for Differential Equations
with an Operator Coefficient Possessing
a Variable Domain in a Banach Space . . 365--396
Abeer Ali Abushama and
Bernard Bialecki Modified Nodal Cubic Spline Collocation
For Poisson's Equation . . . . . . . . . 397--418
Herbert Egger $ \mathcal {Y} $-Scale Regularization 419--436
Erika Hausenblas Finite Element Approximation of
Stochastic Partial Differential
Equations driven by Poisson Random
Measures of Jump Type . . . . . . . . . 437--471
Yan Gong and
Bo Li and
Zhilin Li Immersed-Interface Finite-Element
Methods for Elliptic Interface Problems
with Nonhomogeneous Jump Conditions . . 472--495
Talal Rahman and
Petter BjÒrstad and
Xuejun Xu The Crouzeix--Raviart FE on Nonmatching
Grids with an Approximate Mortar
Condition . . . . . . . . . . . . . . . 496--516
I. G. Graham and
L. Grasedyck and
W. Hackbusch and
S. A. Sauter Optimal Panel-Clustering in the Presence
of Anisotropic Mesh Refinement . . . . . 517--543
Marcus Sarkis and
Henrique Versieux Convergence Analysis for The Numerical
Boundary Corrector for Elliptic
Equations with Rapidly Oscillating
Coefficients . . . . . . . . . . . . . . 545--576
Massimo Fornasier and
Holger Rauhut Recovery Algorithms for Vector-Valued
Data with Joint Sparsity Constraints . . 577--613
Lars Diening and
Christian Kreuzer Linear Convergence of an Adaptive Finite
Element Method for the $p$-Laplacian
Equation . . . . . . . . . . . . . . . . 614--638
Nicolas Besse Convergence of a High-Order
Semi-Lagrangian Scheme with Propagation
of Gradients for the One-Dimensional
Vlasov--Poisson System . . . . . . . . . 639--670
M. H. Annaby and
R. M. Asharabi On Sinc-Based Method in Computing
Eigenvalues of Boundary-Value Problems 671--690
Adrien Blanchet and
Vincent Calvez and
José A. Carrillo Convergence of the Mass-Transport
Steepest Descent Scheme for the
Subcritical Patlak--Keller--Segel Model 691--721
Daniel J. Bates and
Jonathan D. Hauenstein and
Andrew J. Sommese and
Charles W. Wampler II Adaptive Multiprecision Path Tracking 722--746
Yaroslav Kondratyuk and
Rob Stevenson An Optimal Adaptive Finite Element
Method for the Stokes Problem . . . . . 747--775
Alexandre Ern and
Jean-Luc Guermond Discontinuous Galerkin Methods for
Friedrichs' Systems. Part III.
Multifield Theories with Partial
Coercivity . . . . . . . . . . . . . . . 776--804
Daniele A. Di Pietro and
Alexandre Ern and
Jean-Luc Guermond Discontinuous Galerkin Methods for
Anisotropic Semidefinite Diffusion with
Advection . . . . . . . . . . . . . . . 805--831
Zhewei Dai and
Patricia K. Lamm Local Regularization for the Nonlinear
Inverse Autoconvolution Problem . . . . 832--868
Denise Aregba-Driollet and
Maya Briani and
Roberto Natalini Asymptotic High-Order Schemes for $ 2
\times 2 $ Dissipative Hyperbolic
Systems . . . . . . . . . . . . . . . . 869--894
V. M. Devigne and
I. S. Pop and
C. J. van Duijn and
T. Clopeau A Numerical Scheme for the Pore-Scale
Simulation of Crystal Dissolution and
Precipitation in Porous Media . . . . . 895--919
Xuli Han Convexity-Preserving Piecewise Rational
Quartic Interpolation . . . . . . . . . 920--929
Nicholas Hale and
Lloyd N. Trefethen New Quadrature Formulas from Conformal
Maps . . . . . . . . . . . . . . . . . . 930--948
Vivette Girault and
Shuyu Sun and
Mary F. Wheeler and
Ivan Yotov Coupling Discontinuous Galerkin and
Mixed Finite Element Discretizations
using Mortar Finite Elements . . . . . . 949--979
D. Breda and
M. Iannelli and
S. Maset and
R. Vermiglio Stability Analysis of the
Gurtin--MacCamy Model . . . . . . . . . 980--995
Amy L. Bauer and
Raphaël Loub\`ere and
Burton Wendroff On Stability of Staggered Schemes . . . 996--1011
Manuel Castro and
José M. Gallardo and
Juan A. López-GarcÍa and
Carlos Parés Well-Balanced High Order Extensions of
Godunov's Method for Semilinear Balance
Laws . . . . . . . . . . . . . . . . . . 1012--1039
J. M. Sanz-Serna Mollified Impulse Methods for Highly
Oscillatory Differential Equations . . . 1040--1059
Julián Aguirre and
Judith Rivas A Spectral Viscosity Method Based on
Hermite Functions for Nonlinear
Conservation Laws . . . . . . . . . . . 1060--1078
P. Zhuang and
F. Liu and
V. Anh and
I. Turner New Solution and Analytical Techniques
of the Implicit Numerical Method for the
Anomalous Subdiffusion Equation . . . . 1079--1095
Leevan Ling and
Robert Schaback Stable and Convergent Unsymmetric
Meshless Collocation Methods . . . . . . 1097--1115
D. Estep and
V. Ginting and
D. Ropp and
J. N. Shadid and
S. Tavener An A Posteriori--A Priori Analysis of
Multiscale Operator Splitting . . . . . 1116--1146
S. W. Schoombie and
E. Maré High Frequency Induced Instability in
Nyström Methods for the van der Pol
Equation . . . . . . . . . . . . . . . . 1147--1165
Luca Dieci and
Erik S. Van Vleck On the Error in QR Integration . . . . . 1166--1189
Susanne C. Brenner and
Fengyan Li and
Li-Yeng Sung A Locally Divergence-Free Interior
Penalty Method for Two-Dimensional
Curl-Curl Problems . . . . . . . . . . . 1190--1211
Klaus Böhmer On Finite Element Methods for Fully
Nonlinear Elliptic Equations of Second
Order . . . . . . . . . . . . . . . . . 1212--1249
Bernardo Cockburn and
Bo Dong and
Johnny Guzmán Optimal Convergence of the Original DG
Method for the Transport-Reaction
Equation on Special Meshes . . . . . . . 1250--1265
Xiaojun Chen and
Sayed Mahmoud Implicit Runge--Kutta Methods for
Lipschitz Continuous Ordinary
Differential Equations . . . . . . . . . 1266--1280
Runchang Lin and
Zhimin Zhang Natural Superconvergence Points in
Three-Dimensional Finite Elements . . . 1281--1297
Pierre Degond and
Jian-Guo Liu and
Marie-Hél\`ene Vignal Analysis of an Asymptotic Preserving
Scheme for the Euler--Poisson System in
the Quasineutral Limit . . . . . . . . . 1298--1322
V. Faber and
J. Liesen and
P. Tichý The Faber--Manteuffel Theorem for Linear
Operators . . . . . . . . . . . . . . . 1323--1337
Alfredo Bermúdez and
Rodolfo Rodríguez and
Pilar Salgado A Finite Element Method for the
Magnetostatic Problem in Terms of Scalar
Potentials . . . . . . . . . . . . . . . 1338--1363
Bernardo Cockburn and
Johnny Guzmán Error Estimates for the Runge--Kutta
Discontinuous Galerkin Method for the
Transport Equation with Discontinuous
Initial Data . . . . . . . . . . . . . . 1364--1398
L'ubomír Ba\unas and
Sören Bartels and
Andreas Prohl A Convergent Implicit Finite Element
Discretization of the
Maxwell--Landau--Lifshitz--Gilbert
Equation . . . . . . . . . . . . . . . . 1399--1422
Maria Emelianenko and
Lili Ju and
Alexander Rand Nondegeneracy and Weak Global
Convergence of the Lloyd Algorithm in $
\mathbb {R}^d $ . . . . . . . . . . . . 1423--1441
Ricardo G. Durán and
Ariel L. Lombardi Error Estimates for the Raviart--Thomas
Interpolation Under the Maximum Angle
Condition . . . . . . . . . . . . . . . 1442--1453
Nailin Du Finite-Dimensional Approximation
Settings for Infinite-dimensional
Moore--Penrose Inverses . . . . . . . . 1454--1482
Qiang Du and
Maria Emelianenko Uniform Convergence of a Nonlinear
Energy-Based Multilevel Quantization
Scheme . . . . . . . . . . . . . . . . . 1483--1502
Bo Yu and
Bo Dong A Hybrid Polynomial System Solving
Method for Mixed Trigonometric
Polynomial Systems . . . . . . . . . . . 1503--1518
Josef Dick Walsh Spaces Containing Smooth Functions
and Quasi--Monte Carlo Rules of
Arbitrary High Order . . . . . . . . . . 1519--1553
G. M. Coclite and
K. H. Karlsen and
N. H. Risebro A Convergent Finite Difference Scheme
for the Camassa--Holm Equation with
General $ H^1 $ Initial Data . . . . . . 1554--1579
J. Wang and
P. A. Forsyth Maximal Use of Central Differencing for
Hamilton--Jacobi--Bellman PDEs in
Finance . . . . . . . . . . . . . . . . 1580--1601
Natalia Kopteva Maximum Norm A Posteriori Error Estimate
for a $2$D Singularly Perturbed
Semilinear Reaction-Diffusion Problem 1602--1618
E. Lee and
T. A. Manteuffel and
C. R. Westphal Weighted-Norm First-Order System
Least-Squares (FOSLS) for Div/Curl
Systems with Three Dimensional Edge
Singularities . . . . . . . . . . . . . 1619--1639
Z. Cai and
C. R. Westphal A Weighted $H$(div) Least-Squares Method
for Second-Order Elliptic Problems . . . 1640--1651
Huiyuan Li and
Jiachang Sun and
Yuan Xu Discrete Fourier Analysis, Cubature, and
Interpolation on a Hexagon and a
Triangle . . . . . . . . . . . . . . . . 1653--1681
Paola Gervasio Convergence Analysis of High Order
Algebraic Fractional Step Schemes for
Time-Dependent Stokes Equations . . . . 1682--1703
Roland Becker and
Xiaobing Feng and
Andreas Prohl Finite Element Approximations of the
Ericksen--Leslie Model for Nematic
Liquid Crystal Flow . . . . . . . . . . 1704--1731
E. Mordecki and
A. Szepessy and
R. Tempone and
G. E. Zouraris Adaptive Weak Approximation of
Diffusions with Jumps . . . . . . . . . 1732--1768
Eskil Hansen and
Alexander Ostermann Finite Element Runge--Kutta
Discretizations of Porous Medium--Type
Equations . . . . . . . . . . . . . . . 1769--1779
Eric Heinemeyer and
Marko Lindner and
Roland Potthast Convergence and Numerics of a
Multisection Method for Scattering by
Three-Dimensional Rough Surfaces . . . . 1780--1798
Eero Vainikko and
Gennadi Vainikko A Spline Product Quasi-interpolation
Method for Weakly Singular Fredholm
Integral Equations . . . . . . . . . . . 1799--1820
Fuke Wu and
Xuerong Mao Numerical Solutions of Neutral
Stochastic Functional Differential
Equations . . . . . . . . . . . . . . . 1821--1841
J. Salomon and
A. A. Weiss and
B. I. Wohlmuth Energy-Conserving Algorithms for a
Corotational Formulation . . . . . . . . 1842--1866
Thomas Apel and
Gunar Matthies Nonconforming, Anisotropic, Rectangular
Finite Elements of Arbitrary Order for
the Stokes Problem . . . . . . . . . . . 1867--1891
Peter N. Brown and
Homer F. Walker and
Rebecca Wasyk and
Carol S. Woodward On Using Approximate Finite Differences
in Matrix-Free Newton--Krylov Methods 1892--1911
Nathalie Lanson and
Jean-Paul Vila Renormalized Meshfree Schemes I:
Consistency, Stability, and Hybrid
Methods for Conservation Laws . . . . . 1912--1934
Nathalie Lanson and
Jean-Paul Vila Renormalized Meshfree Schemes II:
Convergence for Scalar Conservation Laws 1935--1964
Haotao Cai and
Yuesheng Xu A Fast Fourier--Galerkin Method for
Solving Singular Boundary Integral
Equations . . . . . . . . . . . . . . . 1965--1984
K. Kopotun and
D. Leviatan and
A. V. Prymak Constrained Spline Smoothing . . . . . . 1985--1997
Yan Xu and
Chi-Wang Shu A Local Discontinuous Galerkin Method
for the Camassa--Holm Equation . . . . . 1998--2021
Mechthild Thalhammer High-Order Exponential Operator
Splitting Methods for Time-Dependent
Schrödinger Equations . . . . . . . . . . 2022--2038
Simone Deparis Reduced Basis Error Bound Computation of
Parameter-Dependent Navier--Stokes
Equations by the Natural Norm Approach 2039--2067
D. Estep and
S. Tavener and
T. Wildey A Posteriori Analysis and Improved
Accuracy for an Operator Decomposition
Solution of a Conjugate Heat Transfer
Problem . . . . . . . . . . . . . . . . 2068--2089
Hyea Hyun Kim A BDDC Algorithm for Mortar
Discretization of Elasticity Problems 2090--2111
Roger P. Pawlowski and
Joseph P. Simonis and
Homer F. Walker and
John N. Shadid Inexact Newton Dogleg Methods . . . . . 2112--2132
Hong Wang An Optimal-Order Error Estimate for a
Family of ELLAM-MFEM Approximations to
Porous Medium Flow . . . . . . . . . . . 2133--2152
Clark R. Dohrmann and
Axel Klawonn and
Olof B. Widlund Domain Decomposition for Less Regular
Subdomains: Overlapping Schwarz in Two
Dimensions . . . . . . . . . . . . . . . 2153--2168
Philipp Grohs Smoothness Analysis of Subdivision
Schemes on Regular Grids by Proximity 2169--2182
Hoi Ying Wong and
Jing Zhao An Artificial Boundary Method for
American Option Pricing under the CEV
Model . . . . . . . . . . . . . . . . . 2183--2209
Jing-Mei Qiu and
Chi-Wang Shu Convergence of Godunov-Type Schemes for
Scalar Conservation Laws under Large
Time Steps . . . . . . . . . . . . . . . 2211--2237
Denis Gaidashev and
Dmitry Khmelev On Numerical Algorithms for the Solution
of a Beltrami Equation . . . . . . . . . 2238--2253
Yanping Chen and
Nianyu Yi and
Wenbin Liu A Legendre--Galerkin Spectral Method for
Optimal Control Problems Governed by
Elliptic Equations . . . . . . . . . . . 2254--2275
F. Guillén-González and
J. V. Gutiérrez-Santacreu Conditional Stability and Convergence of
a Fully Discrete Scheme for
Three-Dimensional Navier--Stokes
Equations with Mass Diffusion . . . . . 2276--2308
F. Nobile and
R. Tempone and
C. G. Webster A Sparse Grid Stochastic Collocation
Method for Partial Differential
Equations with Random Input Data . . . . 2309--2345
Hyea Hyun Kim A FETI-DP Formulation of Three
Dimensional Elasticity Problems with
Mortar Discretization . . . . . . . . . 2346--2370
Knut Waagan Convergence Rate of Monotone Numerical
Schemes for Hamilton--Jacobi Equations
with Weak Boundary Conditions . . . . . 2371--2392
Carsten Ebmeyer and
W. B. Liu Finite Element Approximation of the Fast
Diffusion and the Porous Medium
Equations . . . . . . . . . . . . . . . 2393--2410
F. Nobile and
R. Tempone and
C. G. Webster An Anisotropic Sparse Grid Stochastic
Collocation Method for Partial
Differential Equations with Random Input
Data . . . . . . . . . . . . . . . . . . 2411--2442
Marc Ethier and
Yves Bourgault Semi-Implicit Time-Discretization
Schemes for the Bidomain Model . . . . . 2443--2468
Andreas Prohl Convergence of a Finite Element-Based
Space--time Discretization in
Elastodynamics . . . . . . . . . . . . . 2469--2483
Axel Klawonn and
Oliver Rheinbach and
Olof B. Widlund An Analysis of a FETI--DP Algorithm on
Irregular Subdomains in the Plane . . . 2484--2504
Nicholas Hale and
Nicholas J. Higham and
Lloyd N. Trefethen Computing $ A^\alpha, \log (A) $, and
Related Matrix Functions by Contour
Integrals . . . . . . . . . . . . . . . 2505--2523
J. Manuel Cascon and
Christian Kreuzer and
Ricardo H. Nochetto and
Kunibert G. Siebert Quasi-Optimal Convergence Rate for an
Adaptive Finite Element Method . . . . . 2524--2550
Brigitte Bidégaray-Fesquet Stability of FD--TD Schemes for
Maxwell--Debye and Maxwell--Lorentz
Equations . . . . . . . . . . . . . . . 2551--2566
E. E. Ovtchinnikov Jacobi Correction Equation, Line Search,
and Conjugate Gradients in Hermitian
Eigenvalue Computation I: Computing an
Extreme Eigenvalue . . . . . . . . . . . 2567--2592
E. E. Ovtchinnikov Jacobi Correction Equation, Line Search,
and Conjugate Gradients in Hermitian
Eigenvalue Computation II: Computing
Several Extreme Eigenvalues . . . . . . 2593--2619
Shlomo Engelberg and
Eitan Tadmor Recovery of Edges from Spectral Data
with Noise---A New Perspective . . . . . 2620--2635
Jin Ma and
Jie Shen and
Yanhong Zhao On Numerical Approximations of
Forward-Backward Stochastic Differential
Equations . . . . . . . . . . . . . . . 2636--2661
Felix Kwok and
Hamdi A. Tchelepi Convergence of Implicit Monotone Schemes
with Applications in Multiphase Flow in
Porous Media . . . . . . . . . . . . . . 2662--2687
Xin Wen and
Shi Jin The $ \ell^1 $-Error Estimates for a
Hamiltonian-Preserving Scheme for the
Liouville Equation with Piecewise
Constant Potentials . . . . . . . . . . 2688--2714
N. Forcadel An Error Estimate for a New Scheme for
Mean Curvature Motion . . . . . . . . . 2715--2741
Kolja Brix and
Martin Campos Pinto and
Wolfgang Dahmen A Multilevel Preconditioner for the
Interior Penalty Discontinuous Galerkin
Method . . . . . . . . . . . . . . . . . 2742--2768
Luca Formaggia and
Alessandro Veneziani and
Christian Vergara A New Approach to Numerical Solution of
Defective Boundary Value Problems in
Incompressible Fluid Dynamics . . . . . 2769--2794
C. Yalçin Kaya and
J. Lyle Noakes Leapfrog for Optimal Control . . . . . . 2795--2817
Sven Beuchler and
Tino Eibner and
Ulrich Langer Primal and Dual Interface Concentrated
Iterative Substructuring Methods . . . . 2818--2842
Sheng Zhang Analysis of Finite Element Domain
Embedding Methods for Curved Domains
using Uniform Grids . . . . . . . . . . 2843--2866
Kazufumi Ito and
Karl Kunisch Reduced-Order Optimal Control Based on
Approximate Inertial Manifolds for
Nonlinear Dynamical Systems . . . . . . 2867--2891
Gabriel Lord and
Simon J. A. Malham and
Anke Wiese Efficient Strong Integrators for Linear
Stochastic Systems . . . . . . . . . . . 2892--2919
E. Carlini and
M. Falcone and
N. Forcadel and
R. Monneau Convergence of a Generalized
Fast-Marching Method for an Eikonal
Equation with a Velocity-Changing Sign 2920--2952
Pascal Getreuer and
François G. Meyer ENO Multiresolution Schemes with General
Discretizations . . . . . . . . . . . . 2953--2977
Vera Thümmler Numerical Approximation of Relative
Equilibria for Equivariant PDEs . . . . 2978--3005
Leszek Demkowicz and
Jayadeep Gopalakrishnan and
Joachim Schöberl Polynomial Extension Operators. Part I 3006--3031
Franck Boyer and
Florence Hubert Finite Volume Method for $2$D Linear and
Nonlinear Elliptic Problems with
Discontinuities . . . . . . . . . . . . 3032--3070
C. T. Kelley and
Li-Zhi Liao and
Liqun Qi and
Moody T. Chu and
J. P. Reese and
C. Winton Projected Pseudotransient Continuation 3071--3083
O. Kurbanmuradov and
K. Sabelfeld Convergence of Fourier-Wavelet Models
for Gaussian Random Processes . . . . . 3084--3112
Timothy A. Lucas Operator Splitting for an Immunology
Model Using Reaction-Diffusion Equations
with Stochastic Source Terms . . . . . . 3113--3135
Masoumeh Dashti and
James C. Robinson An A Posteriori Condition on the
Numerical Approximations of the
Navier--Stokes Equations for the
Existence of a Strong Solution . . . . . 3136--3150
T. Warburton and
T. Hagstrom Taming the CFL Number for Discontinuous
Galerkin Methods on Structured Meshes 3151--3180
Daniel Peterseim and
Stefan A. Sauter The Composite Mini Element---Coarse Mesh
Computation of Stokes Flows on
Complicated Domains . . . . . . . . . . 3181--3206
Mark Ainsworth and
Richard Rankin Fully Computable Bounds for the Error in
Nonconforming Finite Element
Approximations of Arbitrary Order on
Triangular Elements . . . . . . . . . . 3207--3232
Mihaela Negreanu Convergence of a Semidiscrete Two-Grid
Algorithm for the Controllability of the
$ 1 - d $ Wave Equation . . . . . . . . 3233--3263
Erik G. Boman and
Bruce Hendrickson and
Stephen Vavasis Solving Elliptic Finite Element Systems
in Near-Linear Time with Support
Preconditioners . . . . . . . . . . . . 3264--3284
David Borwein and
Jonathan M. Borwein and
Richard E. Crandall Effective Laguerre Asymptotics . . . . . 3285--3312
Zhendong Luo and
Jing Chen and
I. M. Navon and
Xiaozhong Yang Mixed Finite Element Formulation and
Error Estimates Based on Proper
Orthogonal Decomposition for the
Nonstationary Navier--Stokes Equations 1--19
Paolo Costantini and
Francesca Pelosi Data Approximation Using
Shape-Preserving Parametric Surfaces . . 20--47
Marios Charalambides and
Fabian Waleffe Gegenbauer Tau Methods With and Without
Spurious Eigenvalues . . . . . . . . . . 48--68
Hansjörg Seybold and
Rudolf Hilfer Numerical Algorithm for Calculating the
Generalized Mittag--Leffler Function . . 69--88
Runchang Lin Discontinuous Discretization for
Least-Squares Formulation of Singularly
Perturbed Reaction-Diffusion Problems in
One and Two Dimensions . . . . . . . . . 89--108
Christoph Erath and
Dirk Praetorius A Posteriori Error Estimate and Adaptive
Mesh Refinement for the Cell-Centered
Finite Volume Method for Elliptic
Boundary Value Problems . . . . . . . . 109--135
Hyea Hyun Kim and
Maksymilian Dryja and
Olof B. Widlund A BDDC Method for Mortar Discretizations
Using a Transformation of Basis . . . . 136--157
Andreas Prohl On Pressure Approximation via Projection
Methods for Nonstationary Incompressible
Navier--Stokes Equations . . . . . . . . 158--180
Kristian Debrabant and
Anne KvÆrnÒ B--Series Analysis of Stochastic
Runge--Kutta Methods That Use an
Iterative Scheme to Compute Their
Internal Stage Values . . . . . . . . . 181--203
Weihua Deng Finite Element Method for the Space and
Time Fractional Fokker--Planck Equation 204--226
L. Banjai and
S. Sauter Rapid Solution of the Wave Equation in
Unbounded Domains . . . . . . . . . . . 227--249
Wenfang (Wendy) Cheng and
Xiaoming Wang A Semi-Implicit Scheme for Stationary
Statistical Properties of the Infinite
Prandtl Number Model . . . . . . . . . . 250--270
Mejdi Azaiez and
Jie Shen and
Chuanju Xu and
Qingqu Zhuang A Laguerre--Legendre Spectral Method for
the Stokes Problem in a Semi-Infinite
Channel . . . . . . . . . . . . . . . . 271--292
Reiichiro Kawai Optimal Importance Sampling Parameter
Search for Lévy Processes via Stochastic
Approximation . . . . . . . . . . . . . 293--307
Mattias Sandberg Convergence of the Forward Euler Method
for Nonconvex Differential Inclusions 308--320
Mohammad Saleh Tavazoei and
Mohammad Haeri and
Sadegh Bolouki and
Milad Siami Stability Preservation Analysis for
Frequency-Based Methods in Numerical
Simulation of Fractional Order Systems 321--338
Jean-Luc Guermond and
Bojan Popov $ L^1 $-Approximation of Stationary
Hamilton--Jacobi Equations . . . . . . . 339--362
Ken Alton and
Ian M. Mitchell Fast Marching Methods for Stationary
Hamilton--Jacobi Equations with
Axis-Aligned Anisotropy . . . . . . . . 363--385
Yekaterina Epshteyn and
Alexander Kurganov New Interior Penalty Discontinuous
Galerkin Methods for the Keller--Segel
Chemotaxis Model . . . . . . . . . . . . 386--408
Erik Burman and
Miguel A. Fernández Galerkin Finite Element Methods with
Symmetric Pressure Stabilization for the
Transient Stokes Equations: Stability
and Convergence Analysis . . . . . . . . 409--439
Q. T. Le Gia and
H. N. Mhaskar Localized Linear Polynomial Operators
and Quadrature Formulas on the Sphere 440--466
Shipeng Mao and
Serge Nicaise and
Zhong-Ci Shi On the Interpolation Error Estimates for
$ Q_1 $ Quadrilateral Finite Elements 467--486
Pavel B. Bochev and
Denis Ridzal Rehabilitation of the Lowest-Order
Raviart--Thomas Element on Quadrilateral
Grids . . . . . . . . . . . . . . . . . 487--507
E. Burman and
B. Stamm Low Order Discontinuous Galerkin Methods
for Second Order Elliptic Problems . . . 508--533
R. H. W. Hoppe and
G. Kanschat and
T. Warburton Convergence Analysis of an Adaptive
Interior Penalty Discontinuous Galerkin
Method . . . . . . . . . . . . . . . . . 534--550
L'ubomír Ba\vnas and
Andreas Prohl and
Marián Slodi\vcka Modeling of Thermally Assisted
Magnetodynamics . . . . . . . . . . . . 551--574
U. Hetmaniuk and
P. Knupp Local Anisotropic Interpolation Error
Estimates Based on Directional
Derivatives Along Edges . . . . . . . . 575--595
Javier de Frutos and
Bosco García-Archilla and
Julia Novo Postprocessing Finite-Element Methods
for the Navier--Stokes Equations: The
Fully Discrete Case . . . . . . . . . . 596--621
Jeff Borggaard and
Traian Iliescu and
John Paul Roop A Bounded Artificial Viscosity Large
Eddy Simulation Model . . . . . . . . . 622--645
Andrey Amosov and
Mario Ahues and
Alain Largillier Superconvergence of Some Projection
Approximations for Weakly Singular
Integral Equations Using General Grids 646--674
Hailiang Liu and
Jue Yan The Direct Discontinuous Galerkin (DDG)
Methods for Diffusion Problems . . . . . 675--698
Ramon Codina Finite Element Approximation of the
Three-Field Formulation of the Stokes
Problem Using Arbitrary Interpolations 699--718
Daan Huybrechs and
Ronald Cools On Generalized Gaussian Quadrature Rules
for Singular and Nearly Singular
Integrals . . . . . . . . . . . . . . . 719--739
V. Carey and
D. Estep and
S. Tavener A Posteriori Analysis and Adaptive Error
Control for Multiscale Operator
Decomposition Solution of Elliptic
Systems I: Triangular Systems . . . . . 740--761
Leszek Plaskota and
Grzegorz W. Wasilkowski Uniform Approximation of Piecewise
$r$-Smooth and Globally Continuous
Functions . . . . . . . . . . . . . . . 762--785
Marlis Hochbruck and
Alexander Ostermann and
Julia Schweitzer Exponential Rosenbrock-Type Methods . . 786--803
Alan Demlow Higher-Order Finite Element Methods and
Pointwise Error Estimates for Elliptic
Problems on Surfaces . . . . . . . . . . 805--827
V. Simoncini and
V. Druskin Convergence Analysis of Projection
Methods for the Numerical Solution of
Large Lyapunov Equations . . . . . . . . 828--843
Gilles Aubert and
Pierre Kornprobst Can the Nonlocal Characterization of
Sobolev Spaces by Bourgain et al. Be
Useful for Solving Variational Problems? 844--860
Mario S. Mommer and
Rob Stevenson A Goal-Oriented Adaptive Finite Element
Method with Convergence Rates . . . . . 861--886
G. N. Milstein and
M. V. Tretyakov Practical Variance Reduction via
Regression for Simulating Diffusions . . 887--910
Ming-Jun Lai and
Larry L. Schumaker A Domain Decomposition Method for
Computing Bivariate Spline Fits of
Scattered Data . . . . . . . . . . . . . 911--928
V. J. Ervin and
E. W. Jenkins and
S. Sun Coupled Generalized Nonlinear Stokes
Flow with Flow through a Porous Medium 929--952
Leonid Knizhnerman and
Vladimir Druskin and
Mikhail Zaslavsky On Optimal Convergence Rate of the
Rational Krylov Subspace Reduction for
Electromagnetic Problems in Unbounded
Domains . . . . . . . . . . . . . . . . 953--971
Thorsten Hohage and
Lothar Nannen Hardy Space Infinite Elements for
Scattering and Resonance Problems . . . 972--996
P.-A. Absil and
K. A. Gallivan Accelerated Line-search and Trust-region
Methods . . . . . . . . . . . . . . . . 997--1018
Zhong-Zhi Bai and
Yu-Mei Huang and
Michael K. Ng On Preconditioned Iterative Methods for
Certain Time-Dependent Partial
Differential Equations . . . . . . . . . 1019--1037
Mohamed Amara and
Rabia Djellouli and
Charbel Farhat Convergence Analysis of a Discontinuous
Galerkin Method with Plane Waves and
Lagrange Multipliers for the Solution of
Helmholtz Problems . . . . . . . . . . . 1038--1066
S. Giani and
I. G. Graham A Convergent Adaptive Method for
Elliptic Eigenvalue Problems . . . . . . 1067--1091
Bernardo Cockburn and
Jayadeep Gopalakrishnan The Derivation of Hybridizable
Discontinuous Galerkin Methods for
Stokes Flow . . . . . . . . . . . . . . 1092--1125
Bertrand Maury Numerical Analysis of a Finite
Element/Volume Penalty Method . . . . . 1126--1148
O. Steinbach and
M. Windisch Modified Combined Field Integral
Equations for Electromagnetic Scattering 1149--1167
Christiaan C. Stolk A Fast Method for Linear Waves Based on
Geometrical Optics . . . . . . . . . . . 1168--1194
Benqi Guo and
Jianming Zhang Stable and Compatible Polynomial
Extensions in Three Dimensions and
Applications to the $p$ and $h$-$p$
Finite Element Method . . . . . . . . . 1195--1225
Xiaobing Feng and
Michael Neilan Mixed Finite Element Methods for the
Fully Nonlinear Monge--Amp\`ere Equation
Based on the Vanishing Moment Method . . 1226--1250
Carsten Gräser and
Ralf Kornhuber Nonsmooth Newton Methods for Set-Valued
Saddle Point Problems . . . . . . . . . 1251--1273
Huo-Yuan Duan and
Feng Jia and
Ping Lin and
Roger C. E. Tan The Local $ L^2 $ Projected $ C^0 $
Finite Element Method for Maxwell
Problem . . . . . . . . . . . . . . . . 1274--1303
B. T. Helenbrook On the Existence of Explicit $ h
p$-Finite Element Methods Using
Gauss--Lobatto Integration on the
Triangle . . . . . . . . . . . . . . . . 1304--1318
Bernardo Cockburn and
Jayadeep Gopalakrishnan and
Raytcho Lazarov Unified Hybridization of Discontinuous
Galerkin, Mixed, and Continuous Galerkin
Methods for Second Order Elliptic
Problems . . . . . . . . . . . . . . . . 1319--1365
Liviu I. Ignat and
Enrique Zuazua Numerical Dispersive Schemes for the
Nonlinear Schrödinger Equation . . . . . 1366--1390
Blanca Ayuso and
L. Donatella Marini Discontinuous Galerkin Methods for
Advection-Diffusion-Reaction Problems 1391--1420
Qiang Du and
Desheng Wang and
Liyong Zhu On Mesh Geometry and Stiffness Matrix
Conditioning for General Finite Element
Spaces . . . . . . . . . . . . . . . . . 1421--1444
Mark Embree and
Richard B. Lehoucq Dynamical Systems and Non-Hermitian
Iterative Eigensolvers . . . . . . . . . 1445--1473
Jaroslav Haslinger and
Yves Renard A New Fictitious Domain Approach
Inspired by the Extended Finite Element
Method . . . . . . . . . . . . . . . . . 1474--1499
Qiya Hu and
Xue-Cheng Tai and
Ragnar Winther A Saddle Point Approach to the
Computation of Harmonic Maps . . . . . . 1500--1523
Soorok Ryu and
Hyung-Chun Lee and
Sang Dong Kim First-Order System Least-Squares Methods
for an Optimal Control Problem by the
Stokes Flow . . . . . . . . . . . . . . 1524--1545
A. Kohatsu-Higa and
Kazuhiro Yasuda Estimating Multidimensional Density
Functions Using the Malliavin--Thalmaier
Formula . . . . . . . . . . . . . . . . 1546--1575
Hyea Hyun Kim and
Xuemin Tu A Three-Level BDDC Algorithm for Mortar
Discretizations . . . . . . . . . . . . 1576--1600
Kevin Burrage and
Grant Lythe Accurate Stationary Densities with
Partitioned Numerical Methods for
Stochastic Differential Equations . . . 1601--1618
Jie Shen and
Li-Lian Wang and
Huiyuan Li A Triangular Spectral Element Method
Using Fully Tensorial Rational Basis
Functions . . . . . . . . . . . . . . . 1619--1650
Michael Junk and
Wen-An Yong Weighted $ \mathbb {L}^2 $-Stability of
the Lattice Boltzmann Method . . . . . . 1651--1665
Michael Hintermüller and
Michael Hinze Moreau--Yosida Regularization in State
Constrained Elliptic Control Problems:
Error Estimates and Parameter Adjustment 1666--1683
Raimund Bürger and
Kenneth H. Karlsen and
John D. Towers An Engquist--Osher-Type Scheme for
Conservation Laws with Discontinuous
Flux Adapted to Flux Connections . . . . 1684--1712
Andreas Rößler Second Order Runge--Kutta Methods for Itô
Stochastic Differential Equations . . . 1713--1738
Mihai Anitescu Spectral Finite-Element Methods for
Parametric Constrained Optimization
Problems . . . . . . . . . . . . . . . . 1739--1759
P. Zhuang and
F. Liu and
V. Anh and
I. Turner Numerical Methods for the Variable-Order
Fractional Advection-Diffusion Equation
with a Nonlinear Source Term . . . . . . 1760--1781
B. L. Bihari and
P. N. Brown A Linear Algebraic Analysis of Diffusion
Synthetic Acceleration for the Boltzmann
Transport Equation II: The Simple Corner
Balance Method . . . . . . . . . . . . . 1782--1826
Frank Bauer and
Thorsten Hohage and
Axel Munk Iteratively Regularized Gauss--Newton
Method for Nonlinear Inverse Problems
with Random Noise . . . . . . . . . . . 1827--1846
Torsten Linss Analysis of a System of Singularly
Perturbed Convection-Diffusion Equations
with Strong Coupling . . . . . . . . . . 1847--1862
C. Hager and
B. I. Wohlmuth Analysis of a Space--time Discretization
for Dynamic Elasticity Problems Based on
Mass-Free Surface Elements . . . . . . . 1863--1885
Wenbin Liu and
Ningning Yan Local a Posteriori Error Estimates for
Convex Boundary Control Problems . . . . 1886--1908
Yanren Hou and
Kaitai Li Postprocessing Fourier Galerkin Method
for the Navier--Stokes Equations . . . . 1909--1922
Nicolas Forcadel Comparison Principle for a Generalized
Fast Marching Method . . . . . . . . . . 1923--1951
A. H. Barnett Perturbative Analysis of the Method of
Particular Solutions for Improved
Inclusion of High-Lying Dirichlet
Eigenvalues . . . . . . . . . . . . . . 1952--1970
Santiago Badia and
Ramon Codina Unified Stabilized Finite Element
Formulations for the Stokes and the
Darcy Problems . . . . . . . . . . . . . 1971--2000
Claudio Canuto and
Timo Tonn and
Karsten Urban A Posteriori Error Analysis of the
Reduced Basis Method for Nonaffine
Parametrized Nonlinear PDEs . . . . . . 2001--2022
Luca Dieci and
Luciano Lopez Sliding Motion in Filippov Differential
Systems: Theoretical Results and a
Computational Approach . . . . . . . . . 2023--2051
Vivette Girault and
Béatrice Rivi\`ere DG Approximation of Coupled
Navier--Stokes and Darcy Equations by
Beaver--Joseph--Saffman Interface
Condition . . . . . . . . . . . . . . . 2052--2089
Shangyou Zhang A Family of $ Q_{k + 1, k} \times Q_{k,
k + 1} $ Divergence-Free Finite Elements
on Rectangular Grids . . . . . . . . . . 2090--2107
Xianjuan Li and
Chuanju Xu A Space--time Spectral Method for the
Time Fractional Diffusion Equation . . . 2108--2131
Zhiqiang Cai and
Shun Zhang Recovery-Based Error Estimator for
Interface Problems: Conforming Linear
Elements . . . . . . . . . . . . . . . . 2132--2156
Alan Demlow and
Omar Lakkis and
Charalambos Makridakis A Posteriori Error Estimates in the
Maximum Norm for Parabolic Problems . . 2157--2176
Luigi C. Berselli and
Lars Diening and
Michael R\ocircu\vzi\vcka Optimal Error Estimates for a
Semi-Implicit Euler Scheme for
Incompressible Fluids with Shear
Dependent Viscosities . . . . . . . . . 2177--2202
Jack Schaeffer Higher Order Time Splitting for the
Linear Vlasov Equation . . . . . . . . . 2203--2223
Longjun Shen and
Guixia Lv and
Zhijun Shen A Finite Point Method Based on
Directional Differences . . . . . . . . 2224--2242
Jemal Peradze An Approximate Algorithm for a Kirchhoff
Wave Equation . . . . . . . . . . . . . 2243--2268
S. M. Wise and
C. Wang and
J. S. Lowengrub An Energy-Stable and Convergent
Finite-Difference Scheme for the Phase
Field Crystal Equation . . . . . . . . . 2269--2288
Olivier Bokanowski and
Benjamin Bruder and
Stefania Maroso and
Hasnaa Zidani Numerical Approximation for a
Superreplication Problem under Gamma
Constraints . . . . . . . . . . . . . . 2289--2320
Zhongying Chen and
Bin Wu and
Yuesheng Xu Fast Multilevel Augmentation Methods for
Solving Hammerstein Equations . . . . . 2321--2346
Rob Haelterman and
Joris Degroote and
Dirk Van Heule and
Jan Vierendeels The Quasi-Newton Least Squares Method: A
New and Fast Secant Method Analyzed for
Linear Systems . . . . . . . . . . . . . 2347--2368
Francesca Rapetti and
Alain Bossavit Whitney Forms of Higher Degree . . . . . 2369--2386
Andreas Veeser and
Rüdiger Verfürth Explicit Upper Bounds for Dual Norms of
Residuals . . . . . . . . . . . . . . . 2387--2405
Fabio Camilli and
Espen R. Jakobsen A Finite Element Like Scheme for
Integro-Partial Differential
Hamilton--Jacobi--Bellman Equations . . 2407--2431
Erwin Hernández and
Enrique Otárola A Locking-Free FEM in Active Vibration
Control of a Timoshenko Beam . . . . . . 2432--2454
Matthew Dobson and
Mitchell Luskin An Optimal Order Error Analysis of the
One-Dimensional Quasicontinuum
Approximation . . . . . . . . . . . . . 2455--2475
J. Thomas Beale Smoothing Properties of Implicit Finite
Difference Methods for a Diffusion
Equation in Maximum Norm . . . . . . . . 2476--2495
Qun Lin and
Lung-an Ying Interval Inclusion Computation for the
Solutions of the Burgers Equation . . . 2496--2517
János Karátson and
Sergey Korotov An Algebraic Discrete Maximum Principle
in Hilbert Space with Applications to
Nonlinear Cooperative Elliptic Systems 2518--2549
C. Ortner A Posteriori Existence in Numerical
Computations . . . . . . . . . . . . . . 2550--2577
Benqi Guo Approximation Theory for the $P$-Version
of the Finite Element Method in Three
Dimensions. Part II: Convergence of the
$P$ Version of the Finite Element Method 2578--2611
Andrea Cangiani and
Gianmarco Manzini and
Alessandro Russo Convergence Analysis of the Mimetic
Finite Difference Method for Elliptic
Problems . . . . . . . . . . . . . . . . 2612--2637
Franz Peherstorfer Gauss--Turán Quadrature Formulas:
Asymptotics of Weights . . . . . . . . . 2638--2659
David Kay and
Vanessa Styles and
Endre Süli Discontinuous Galerkin Finite Element
Approximation of the Cahn--Hilliard
Equation with Convection . . . . . . . . 2660--2685
Bernardo Cockburn and
Johnny Guzmán and
See-Chew Soon and
Henry K. Stolarski An Analysis of the Embedded
Discontinuous Galerkin Method for
Second-Order Elliptic Problems . . . . . 2686--2707
David P. Nicholls and
Jie Shen A Rigorous Numerical Analysis of the
Transformed Field Expansion Method . . . 2708--2734
Joachim Schöberl and
Rolf Stenberg Multigrid Methods for a Stabilized
Reissner--Mindlin Plate Formulation . . 2735--2751
D. C. Antonopoulou and
V. A. Dougalis and
G. E. Zouraris Galerkin Methods for Parabolic and
Schrödinger Equations with Dynamical
Boundary Conditions and Applications to
Underwater Acoustics . . . . . . . . . . 2752--2781
Pascal Omnes and
Yohan Penel and
Yann Rosenbaum A Posteriori Error Estimation for the
Discrete Duality Finite Volume
Discretization of the Laplace Equation 2782--2807
F. Castella and
P. Chartier and
E. Faou An Averaging Technique for Highly
Oscillatory Hamiltonian Problems . . . . 2808--2837
Alessandro Veneziani A Note on the Consistency and Stability
Properties of Yosida Fractional Step
Schemes for the Unsteady Stokes
Equations . . . . . . . . . . . . . . . 2838--2843
Jean-François Coulombel Stability of Finite Difference Schemes
for Hyperbolic Initial Boundary Value
Problems . . . . . . . . . . . . . . . . 2844--2871
Xiaobing Feng and
Haijun Wu Discontinuous Galerkin Methods for the
Helmholtz Equation with Large Wave
Number . . . . . . . . . . . . . . . . . 2872--2896
Clark R. Dohrmann and
Olof B. Widlund An Overlapping Schwarz Algorithm for
Almost Incompressible Elasticity . . . . 2897--2923
Mario Arioli and
Daniel Loghin Discrete Interpolation Norms with
Applications . . . . . . . . . . . . . . 2924--2951
Xiaobing Feng and
Michael Neilan A Modified Characteristic Finite Element
Method for a Fully Nonlinear Formulation
of the Semigeostrophic Flow Equations 2952--2981
Chu-Li Fu and
Zhi-Liang Deng and
Xiao-Li Feng and
Fang-Fang Dou A Modified Tikhonov Regularization for
Stable Analytic Continuation . . . . . . 2982--3000
Olivier Bokanowski and
Stefania Maroso and
Hasnaa Zidani Some Convergence Results for Howard's
Algorithm . . . . . . . . . . . . . . . 3001--3026
Frank S. Attia and
Zhiqiang Cai and
Gerhard Starke First-Order System Least Squares for the
Signorini Contact Problem in Linear
Elasticity . . . . . . . . . . . . . . . 3027--3043
Christian Gross and
Rolf Krause On the Convergence of Recursive
Trust-Region Methods for Multiscale
Nonlinear Optimization and Applications
to Nonlinear Mechanics . . . . . . . . . 3044--3069
Mitchell Luskin and
Christoph Ortner An Analysis of Node-Based Cluster
Summation Rules in the Quasicontinuum
Method . . . . . . . . . . . . . . . . . 3070--3086
M. Ben-Artzi and
I. Chorev and
J.-P. Croisille and
D. Fishelov A Compact Difference Scheme for the
Biharmonic Equation in Planar Irregular
Domains . . . . . . . . . . . . . . . . 3087--3108
Stefano Berrone A Local-in-Space-timestep Approach to a
Finite Element Discretization of the
Heat Equation with a Posteriori
Estimates . . . . . . . . . . . . . . . 3109--3138
Néstor E. Aguilera and
Pedro Morin On Convex Functions and the Finite
Element Method . . . . . . . . . . . . . 3139--3157
Holger Wendland Divergence-Free Kernel Methods for
Approximating the Stokes Problem . . . . 3158--3179
R. Verfürth A Note on Constant-Free a Posteriori
Error Estimates . . . . . . . . . . . . 3180--3194
Masatake Hirao and
Masanori Sawa On Minimal Cubature Formulae of Small
Degree for Spherically Symmetric
Integrals . . . . . . . . . . . . . . . 3195--3211
Edward J. Fuselier and
Grady B. Wright Stability and Error Estimates for Vector
Field Interpolation and Decomposition on
the Sphere with RBFs . . . . . . . . . . 3213--3239
Bo Dong and
Chi-Wang Shu Analysis of a Local Discontinuous
Galerkin Method for Linear
Time-Dependent Fourth-Order Problems . . 3240--3268
Rajen K. Sinha and
Richard E. Ewing and
Raytcho D. Lazarov Mixed Finite Element Approximations of
Parabolic Integro-Differential Equations
with Nonsmooth Initial Data . . . . . . 3269--3292
Leszek Demkowicz and
Jayadeep Gopalakrishnan and
Joachim Schöberl Polynomial Extension Operators. Part II 3293--3324
Mingchao Cai and
Mo Mu and
Jinchao Xu Numerical Solution to a Mixed
Navier--Stokes/Darcy Model by the
Two-Grid Approach . . . . . . . . . . . 3325--3338
Maxim A. Olshanskii and
Arnold Reusken and
Jörg Grande A Finite Element Method for Elliptic
Equations on Surfaces . . . . . . . . . 3339--3358
Sheehan Olver GMRES for the Differentiation Operator 3359--3373
Alain Bensoussan and
Laurent Mertz and
Olivier Pironneau and
Janos Turi An Ultra Weak Finite Element Method as
an Alternative to a Monte Carlo Method
for an Elasto-Plastic Problem with Noise 3374--3396
Massimo Fornasier and
Carola-Bibiane Schönlieb Subspace Correction Methods for Total
Variation and $ \ell_1$-Minimization . . 3397--3428
Bernard Bialecki and
Ryan I. Fernandes An Alternating Direction Implicit
Backward Differentiation Orthogonal
Spline Collocation Method for Linear
Variable Coefficient Parabolic Equations 3429--3450
Francisco-Javier Sayas The Validity of Johnson--Nédélec's
BEM--FEM Coupling on Polygonal
Interfaces . . . . . . . . . . . . . . . 3451--3463
Oliver Junge and
Péter Koltai Discretization of the Frobenius--Perron
Operator Using a Sparse Haar Tensor
Basis: The Sparse Ulam Method . . . . . 3464--3485
Sören Bartels Semi-Implicit Approximation of Wave Maps
into Smooth or Convex Surfaces . . . . . 3486--3506
Todd A. Oliver and
David L. Darmofal Analysis of Dual Consistency for
Discontinuous Galerkin Discretizations
of Source Terms . . . . . . . . . . . . 3507--3525
Jeffrey M. Connors and
Jason S. Howell and
William J. Layton Partitioned Time Stepping for a
Parabolic Two Domain Problem . . . . . . 3526--3549
Patrick Hild and
Vanessa Lleras Residual Error Estimators for Coulomb
Friction . . . . . . . . . . . . . . . . 3550--3583
Erik Burman A Posteriori Error Estimation for
Interior Penalty Finite Element
Approximations of the Advection-Reaction
Equation . . . . . . . . . . . . . . . . 3584--3607
Daniel J. Bates and
Jonathan D. Hauenstein and
Chris Peterson and
Andrew J. Sommese A Numerical Local Dimension Test for
Points on the Solution Set of a System
of Polynomial Equations . . . . . . . . 3608--3623
J. Galvis and
M. Sarkis Approximating Infinity-Dimensional
Stochastic Darcy's Equations without
Uniform Ellipticity . . . . . . . . . . 3624--3651
Gabriel R. Barrenechea and
Leopoldo P. Franca and
Frédéric Valentin A Symmetric Nodal Conservative Finite
Element Method for the Darcy Equation 3652--3677
Thomas Hagstrom and
Timothy Warburton Complete Radiation Boundary Conditions:
Minimizing the Long Time Error Growth of
Local Methods . . . . . . . . . . . . . 3678--3704
Arnaud Debussche and
Erwan Faou Modified Energy for Split-Step Methods
Applied to the Linear Schrödinger
Equation . . . . . . . . . . . . . . . . 3705--3719
Sören Bartels and
Max Jensen and
Rüdiger Müller Discontinuous Galerkin Finite Element
Convergence for Incompressible Miscible
Displacement Problems of Low Regularity 3720--3743
Yanzhao Cao and
Bin Wu and
Yuesheng Xu A Fast Collocation Method for Solving
Stochastic Integral Equations . . . . . 3744--3767
Lanshan Han and
Alok Tiwari and
M. Kanat Camlibel and
Jong-Shi Pang Convergence of Time-Stepping Schemes for
Passive and Extended Linear
Complementarity Systems . . . . . . . . 3768--3796
W. Hundsdorfer and
A. Mozartova and
M. N. Spijker Stepsize Conditions for Boundedness in
Numerical Initial Value Problems . . . . 3797--3819
Eric T. Chung and
Björn Engquist Optimal Discontinuous Galerkin Methods
for the Acoustic Wave Equation in Higher
Dimensions . . . . . . . . . . . . . . . 3820--3848
Bernhard Beckermann and
Lothar Reichel Error Estimates and Evaluation of Matrix
Functions via the Faber Transform . . . 3849--3883
Filip Rindler Approximation of Rate-Independent
Optimal Control Problems . . . . . . . . 3884--3909
Mark Ainsworth and
Hafiz Abdul Wajid Dispersive and Dissipative Behavior of
the Spectral Element Method . . . . . . 3910--3937
Pavel B. Bochev and
Denis Ridzal An Optimization-Based Approach for the
Design of PDE Solution Algorithms . . . 3938--3955
Bruno Després Uniform Asymptotic Stability of Strang's
Explicit Compact Schemes for Linear
Advection . . . . . . . . . . . . . . . 3956--3976
Alexei Bespalov and
Norbert Heuer Optimal Error Estimation for $ \bf
H({\rm curl}) $-Conforming
$p$-Interpolation in Two Dimensions . . 3977--3989
Carlo D'Angelo and
Paolo Zunino A Finite Element Method Based on
Weighted Interior Penalties for
Heterogeneous Incompressible Flows . . . 3990--4020