EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues ESAIM: M2AN, 21 2 (1987) 199-238 Article references

Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

New a posteriori error estimates for hp version of finite element methods of nonlinear parabolic optimal control problems

Zuliang Lu, Hongyan Liu, Chunjuan Hou and Longzhou Cao
Journal of Inequalities and Applications 2016 (1) (2016)
https://doi.org/10.1186/s13660-016-0994-3

A priori hp-estimates for discontinuous Galerkin approximations to linear hyperbolic integro-differential equations

Samir Karaa, Amiya K. Pani and Sangita Yadav
Applied Numerical Mathematics 96 1 (2015)
https://doi.org/10.1016/j.apnum.2015.04.006

An $$hp$$ h p finite element adaptive scheme to solve the Poisson problem on curved domains

M. G. Armentano, C. Padra and M. Scheble
Computational and Applied Mathematics 34 (2) 705 (2015)
https://doi.org/10.1007/s40314-014-0133-z

Mixed finite element methods for two-body contact problems

Andreas Schröder, Heiko Kleemann and Heribert Blum
Journal of Computational and Applied Mathematics 283 58 (2015)
https://doi.org/10.1016/j.cam.2014.11.040

A unified a posteriori error estimate of local discontinuous Galerkin approximations for reactive transport problems

Jiming Yang
Indian Journal of Pure and Applied Mathematics 46 (6) 759 (2015)
https://doi.org/10.1007/s13226-015-0160-5

A new posteriori error estimates for a discontinuous Galerkin method for a reaction–diffusion problem

Jiwei Cao and Zhihao Ge
Applied Mathematics and Computation 256 735 (2015)
https://doi.org/10.1016/j.amc.2015.01.032

hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes

Andrea Cangiani, Emmanuil H. Georgoulis and Paul Houston
Mathematical Models and Methods in Applied Sciences 24 (10) 2009 (2014)
https://doi.org/10.1142/S0218202514500146

A posteriori error estimates for control problems governed by nonlinear elliptic equations in hp-FEM

Yanping Chen and Yijie Lin
Applied Mathematics and Computation 238 163 (2014)
https://doi.org/10.1016/j.amc.2014.03.053

Upwind discontinuous Galerkin methods with mass conservation of both phases for incompressible two‐phase flow in porous media

Jisheng Kou and Shuyu Sun
Numerical Methods for Partial Differential Equations 30 (5) 1674 (2014)
https://doi.org/10.1002/num.21817

Reprint of “Construction of polynomial extensions in two dimensions and application to theh-pfinite element method”

Benqi Guo and Jianming Zhang
Journal of Computational and Applied Mathematics 265 151 (2014)
https://doi.org/10.1016/j.cam.2014.01.013

Construction of polynomial extensions in two dimensions and application to theh-pfinite element method

Benqi Guo and Jianming Zhang
Journal of Computational and Applied Mathematics 261 249 (2014)
https://doi.org/10.1016/j.cam.2013.09.053

HIGHER ORDER DISCONTINUOUS GALERKIN FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS

Mi Ray Ohm, Hyun Young Lee and Jun Yong Shin
Journal of the Korea Society for Industrial and Applied Mathematics 18 (4) 337 (2014)
https://doi.org/10.12941/jksiam.2014.18.337

A study on directional resistivity logging-while-drilling based on self-adaptive hp-FEM

Dejun Liu, Hui Li, Yingying Zhang, Gengxue Zhu and Qinghui Ai
Acta Geophysica 62 (6) 1328 (2014)
https://doi.org/10.2478/s11600-014-0212-y

Uniqueness of numerical solutions to nonlinear parabolic equations by a fully implicit discontinuous Galerkin method

Lunji Song and Jinhu Ma
Applied Mathematics Letters 37 77 (2014)
https://doi.org/10.1016/j.aml.2014.05.016

DISCONTINUOUS GALERKIN METHOD FOR NONLINEAR PARABOLIC PROBLEMS WITH MIXED BOUNDARY CONDITION

Mi Ray Ohm, Hyun Yong Lee and Jun Yong Shin
Journal of applied mathematics & informatics 32 (5_6) 585 (2014)
https://doi.org/10.14317/jami.2014.585

A Comparison of hp -Adaptive Strategies for Elliptic Partial Differential Equations

William F. Mitchell and Marjorie A. McClain
ACM Transactions on Mathematical Software 41 (1) 1 (2014)
https://doi.org/10.1145/2629459

Discontinuous Galerkin Discretization and $hp$-Refinement for the Resolution of the Neutron Transport Equation

D. Fournier, R. Herbin and R. Le Tellier
SIAM Journal on Scientific Computing 35 (2) A936 (2013)
https://doi.org/10.1137/110844581

$hp$-Version Composite Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains

Paola F. Antonietti, Stefano Giani and Paul Houston
SIAM Journal on Scientific Computing 35 (3) A1417 (2013)
https://doi.org/10.1137/120877246

L 2-error analysis of discontinuous Galerkin approximations for nonlinear Sobolev equations

Mi Ray Ohm, Hyun Young Lee and Jun Yong Shin
Japan Journal of Industrial and Applied Mathematics 30 (1) 91 (2013)
https://doi.org/10.1007/s13160-012-0096-7

A discontinuous Galerkin finite element method for swelling model of polymer gels

Huanrong Li and Yukun Li
Journal of Mathematical Analysis and Applications 398 (1) 11 (2013)
https://doi.org/10.1016/j.jmaa.2012.08.033

SPEED: SPectral Elements in Elastodynamics with Discontinuous Galerkin: a non‐conforming approach for 3D multi‐scale problems

I. Mazzieri, M. Stupazzini, R. Guidotti and C. Smerzini
International Journal for Numerical Methods in Engineering 95 (12) 991 (2013)
https://doi.org/10.1002/nme.4532

Preasymptotic Error Analysis of CIP-FEM and FEM for Helmholtz Equation with High Wave Number. Part II: $hp$ Version

Lingxue Zhu and Haijun Wu
SIAM Journal on Numerical Analysis 51 (3) 1828 (2013)
https://doi.org/10.1137/120874643

Finite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems

Clemens Pechstein
Lecture Notes in Computational Science and Engineering, Finite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems 90 247 (2013)
https://doi.org/10.1007/978-3-642-23588-7_5

Finite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems

Clemens Pechstein
Lecture Notes in Computational Science and Engineering, Finite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems 90 157 (2013)
https://doi.org/10.1007/978-3-642-23588-7_3

Finite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems

Clemens Pechstein
Lecture Notes in Computational Science and Engineering, Finite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems 90 1 (2013)
https://doi.org/10.1007/978-3-642-23588-7_1

Finite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems

Clemens Pechstein
Lecture Notes in Computational Science and Engineering, Finite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems 90 63 (2013)
https://doi.org/10.1007/978-3-642-23588-7_2

LOCAL CHEBYSHEV PROJECTION–INTERPOLATION OPERATOR AND APPLICATION TO THE h–p VERSION OF THE FINITE ELEMENT METHOD IN THREE DIMENSIONS

BENQI GUO and LIJUN YI
Mathematical Models and Methods in Applied Sciences 23 (05) 777 (2013)
https://doi.org/10.1142/S0218202512500601

Convergence of Discontinuous Galerkin Methods for Incompressible Two-Phase Flow in Heterogeneous Media

Jisheng Kou and Shuyu Sun
SIAM Journal on Numerical Analysis 51 (6) 3280 (2013)
https://doi.org/10.1137/120898358

Quasi-optimal A Priori Interface Error Bounds and A Posteriori Estimates for the Interior Penalty Method

Christian Waluga and Barbara Wohlmuth
SIAM Journal on Numerical Analysis 51 (6) 3259 (2013)
https://doi.org/10.1137/120888405

Domain Decomposition Methods in Science and Engineering XX

Herbert Egger and Christian Waluga
Lecture Notes in Computational Science and Engineering, Domain Decomposition Methods in Science and Engineering XX 91 663 (2013)
https://doi.org/10.1007/978-3-642-35275-1_79

Efficient simulation of cardiac electrical propagation using high-order finite elements II: Adaptive p-version

Christopher J. Arthurs, Martin J. Bishop and David Kay
Journal of Computational Physics 253 443 (2013)
https://doi.org/10.1016/j.jcp.2013.07.011

A Posteriori Error Estimates of a Combined Mixed Finite Element and Discontinuous Galerkin Method for a Kind of Compressible Miscible Displacement Problems

Jiming Yang and Zhiguang Xiong
Advances in Applied Mathematics and Mechanics 5 (2) 163 (2013)
https://doi.org/10.4208/aamm.11-m1140

A spectral collocation method for eigenvalue problems of compact integral operators

Can Huang, Hailong Guo and Zhimin Zhang
Journal of Integral Equations and Applications 25 (1) (2013)
https://doi.org/10.1216/JIE-2013-25-1-79

Finite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems

Clemens Pechstein
Lecture Notes in Computational Science and Engineering, Finite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems 90 215 (2013)
https://doi.org/10.1007/978-3-642-23588-7_4

A Priori Error Analysis of Stochastic Galerkin Mixed Approximations of Elliptic PDEs with Random Data

Alexei Bespalov, Catherine E. Powell and David Silvester
SIAM Journal on Numerical Analysis 50 (4) 2039 (2012)
https://doi.org/10.1137/110854898

Non-conforming high order approximations of the elastodynamics equation

P.F. Antonietti, I. Mazzieri, A. Quarteroni and F. Rapetti
Computer Methods in Applied Mechanics and Engineering 209-212 212 (2012)
https://doi.org/10.1016/j.cma.2011.11.004

Higher order weakly over-penalized symmetric interior penalty methods

Susanne C. Brenner, Luke Owens and Li-Yeng Sung
Journal of Computational and Applied Mathematics 236 (11) 2883 (2012)
https://doi.org/10.1016/j.cam.2012.01.025

An Unfitted Discontinuous Galerkin Method Applied to Elliptic Interface Problems

Ralf Massjung
SIAM Journal on Numerical Analysis 50 (6) 3134 (2012)
https://doi.org/10.1137/090763093

Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

Alexey Chernov
Applied Numerical Mathematics 62 (4) 360 (2012)
https://doi.org/10.1016/j.apnum.2011.06.015

Finite Elements for Elliptic Problems with Highly Varying, Nonperiodic Diffusion Matrix

D. Peterseim and S. Sauter
Multiscale Modeling & Simulation 10 (3) 665 (2012)
https://doi.org/10.1137/10081839X

ERROR ESTIMATES OF SEMIDISCRETE DISCONTINUOUS GALERKIN APPROXIMATIONS FOR THE VISCOELASTICITY-TYPE EQUATION

Mi-Ray Ohm, Hyun-Young Lee and Jun-Yong Shin
Bulletin of the Korean Mathematical Society 49 (4) 829 (2012)
https://doi.org/10.4134/BKMS.2012.49.4.829

Efficient simulation of cardiac electrical propagation using high order finite elements

Christopher J. Arthurs, Martin J. Bishop and David Kay
Journal of Computational Physics 231 (10) 3946 (2012)
https://doi.org/10.1016/j.jcp.2012.01.037

Analysis of an $hp$-Nonconforming Discontinuous Galerkin Spectral Element Method for Wave Propagation

Tan Bui-Thanh and Omar Ghattas
SIAM Journal on Numerical Analysis 50 (3) 1801 (2012)
https://doi.org/10.1137/110828010

hp‐adaptive extended finite element method

A. Byfut and A. Schröder
International Journal for Numerical Methods in Engineering 89 (11) 1392 (2012)
https://doi.org/10.1002/nme.3293

Mixed Finite Element Methods of Higher-Order for Model Contact Problems

Andreas Schröder
SIAM Journal on Numerical Analysis 49 (6) 2323 (2011)
https://doi.org/10.1137/090770072

Error estimate of fully discrete discontinuous Galerkin approximation for the viscoelasticity type equation

Mi Ray Ohm, Hyun Young Lee and Jun Yong Shin
Journal of Applied Mathematics and Computing 37 (1-2) 473 (2011)
https://doi.org/10.1007/s12190-010-0445-0

An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations

Amiya K. Pani and Sangita Yadav
Journal of Scientific Computing 46 (1) 71 (2011)
https://doi.org/10.1007/s10915-010-9384-z

hp Adaptive finite elements based on derivative recovery and superconvergence

Randolph E. Bank and Hieu Nguyen
Computing and Visualization in Science 14 (6) 287 (2011)
https://doi.org/10.1007/s00791-012-0179-7

A posteriori error of a discontinuous Galerkin scheme for compressible miscible displacement problems with molecular diffusion and dispersion

Jiming Yang
International Journal for Numerical Methods in Fluids 65 (7) 781 (2011)
https://doi.org/10.1002/fld.2208

An hp finite element adaptive scheme to solve the Laplace model for fluid–solid vibrations

M.G. Armentano, C. Padra, R. Rodríguez and M. Scheble
Computer Methods in Applied Mechanics and Engineering 200 (1-4) 178 (2011)
https://doi.org/10.1016/j.cma.2010.08.003

A posteriori error estimates for hp finite element solutions of convex optimal control problems

Yanping Chen and Yijie Lin
Journal of Computational and Applied Mathematics 235 (12) 3435 (2011)
https://doi.org/10.1016/j.cam.2011.02.004

A newH(div)-conformingp-interpolation operator in two dimensions

Alexei Bespalov and Norbert Heuer
ESAIM: Mathematical Modelling and Numerical Analysis 45 (2) 255 (2011)
https://doi.org/10.1051/m2an/2010039

Local Jacobi Operators and Applications to thep-Version of Finite Element Method in Two Dimensions

Benqi Guo and Ivo Babuška
SIAM Journal on Numerical Analysis 48 (1) 147 (2010)
https://doi.org/10.1137/090747208

Error estimation and anisotropic mesh refinement for 3d laminar aerodynamic flow simulations

Tobias Leicht and Ralf Hartmann
Journal of Computational Physics 229 (19) 7344 (2010)
https://doi.org/10.1016/j.jcp.2010.06.019

A priori error analysis of a discontinuous Galerkin approximation for a kind of compressible miscible displacement problems

JiMing Yang and YanPing Chen
Science China Mathematics 53 (10) 2679 (2010)
https://doi.org/10.1007/s11425-010-3128-2

Analysis of hp discontinuous Galerkin methods for incompressible two-phase flow

Yekaterina Epshteyn and Beatrice Rivière
Journal of Computational and Applied Mathematics 225 (2) 487 (2009)
https://doi.org/10.1016/j.cam.2008.08.026

Approximation Theory for the P-Version of the Finite Element Method in Three Dimensions Part II: Convergence of thePVersion of the Finite Element Method

Benqi Guo
SIAM Journal on Numerical Analysis 47 (4) 2578 (2009)
https://doi.org/10.1137/070701066

On L2-error estimate for nonsymmetric interior penalty Galerkin approximation to linear elliptic problems with nonhomogeneous Dirichlet data

Thirupathi Gudi, Neela Nataraj and Amiya K. Pani
Journal of Computational and Applied Mathematics 228 (1) 30 (2009)
https://doi.org/10.1016/j.cam.2008.08.036

New Interior Penalty Discontinuous Galerkin Methods for the Keller–Segel Chemotaxis Model

Yekaterina Epshteyn and Alexander Kurganov
SIAM Journal on Numerical Analysis 47 (1) 386 (2009)
https://doi.org/10.1137/07070423X

Optimal Error Estimation for ${\bfH}({\rmcurl})$-Conformingp-Interpolation in Two Dimensions

Alexei Bespalov and Norbert Heuer
SIAM Journal on Numerical Analysis 47 (5) 3977 (2009)
https://doi.org/10.1137/090753802

Fully Discrete Analysis of a Discontinuous Finite Element Method for the Keller-Segel Chemotaxis Model

Yekaterina Epshteyn and Ahmet Izmirlioglu
Journal of Scientific Computing 40 (1-3) 211 (2009)
https://doi.org/10.1007/s10915-009-9281-5

Stable and Compatible Polynomial Extensions in Three Dimensions and Applications to thepandh-pFinite Element Method

Benqi Guo and Jianming Zhang
SIAM Journal on Numerical Analysis 47 (2) 1195 (2009)
https://doi.org/10.1137/070688006

A Locally Conservative Finite Element Method Based on Piecewise Constant Enrichment of the Continuous Galerkin Method

Shuyu Sun and Jiangguo Liu
SIAM Journal on Scientific Computing 31 (4) 2528 (2009)
https://doi.org/10.1137/080722953

n-Widths, sup–infs, and optimality ratios for the k-version of the isogeometric finite element method

John A. Evans, Yuri Bazilevs, Ivo Babuška and Thomas J.R. Hughes
Computer Methods in Applied Mechanics and Engineering 198 (21-26) 1726 (2009)
https://doi.org/10.1016/j.cma.2009.01.021

hp-Discontinuous Galerkin methods for strongly nonlinear elliptic boundary value problems

Thirupathi Gudi, Neela Nataraj and Amiya K. Pani
Numerische Mathematik 109 (2) 233 (2008)
https://doi.org/10.1007/s00211-008-0137-y

A coupling of mixed and discontinuous Galerkin finite-element methods for poroelasticity

Phillip Joseph Phillips and Mary F. Wheeler
Computational Geosciences 12 (4) 417 (2008)
https://doi.org/10.1007/s10596-008-9082-1

Analysis of a semidiscrete discontinuous Galerkin scheme for compressible miscible displacement problem

Mingrong Cui
Journal of Computational and Applied Mathematics 214 (2) 617 (2008)
https://doi.org/10.1016/j.cam.2007.03.019

Mixed Discontinuous Galerkin Finite Element Method for the Biharmonic Equation

Thirupathi Gudi, Neela Nataraj and Amiya K. Pani
Journal of Scientific Computing 37 (2) 139 (2008)
https://doi.org/10.1007/s10915-008-9200-1

Error estimates for a discontinuous Galerkin method with interior penalties applied to nonlinear Sobolev equations

Tongjun Sun and Danping Yang
Numerical Methods for Partial Differential Equations 24 (3) 879 (2008)
https://doi.org/10.1002/num.20294

Analysis and application of the IIPG method to quasilinear nonstationary convection–diffusion problems

Vít Dolejší
Journal of Computational and Applied Mathematics 222 (2) 251 (2008)
https://doi.org/10.1016/j.cam.2007.10.055

Thehp-version of the boundary element method with quasi-uniform meshes in three dimensions

Alexei Bespalov and Norbert Heuer
ESAIM: Mathematical Modelling and Numerical Analysis 42 (5) 821 (2008)
https://doi.org/10.1051/m2an:2008025

Polynomial Extension Operators. Part I

Leszek Demkowicz, Jayadeep Gopalakrishnan and Joachim Schöberl
SIAM Journal on Numerical Analysis 46 (6) 3006 (2008)
https://doi.org/10.1137/070698786

A priori error estimates for interior penalty discontinuous Galerkin method applied to nonlinear Sobolev equations

Tongjun Sun and Danping Yang
Applied Mathematics and Computation 200 (1) 147 (2008)
https://doi.org/10.1016/j.amc.2007.10.053

The hp‐version of the BEM with quasi‐uniform meshes for a three‐dimensional crack problem: The case of a smooth crack having smooth boundary curve

Alexei Bespalov
Numerical Methods for Partial Differential Equations 24 (4) 1159 (2008)
https://doi.org/10.1002/num.20311

An iterative substructuring method for the hp‐version of the BEM on quasi‐uniform triangular meshes

Norbert Heuer, Florian Leydecker and Ernst P. Stephan
Numerical Methods for Partial Differential Equations 23 (4) 879 (2007)
https://doi.org/10.1002/num.20259

Discontinuous Galerkin Methods for Quasi‐Linear Elliptic Problems of Nonmonotone Type

Thirupathi Gudi and Amiya K. Pani
SIAM Journal on Numerical Analysis 45 (1) 163 (2007)
https://doi.org/10.1137/050643362

A combined mixed and discontinuous Galerkin method for compressible miscible displacement problem in porous media

Mingrong Cui
Journal of Computational and Applied Mathematics 198 (1) 19 (2007)
https://doi.org/10.1016/j.cam.2005.11.021

The p-version of the boundary element method for weakly singular operators on piecewise plane open surfaces

Alexei Bespalov and Norbert Heuer
Numerische Mathematik 106 (1) 69 (2007)
https://doi.org/10.1007/s00211-006-0058-6

hp-Version a priori Error Analysis of Interior Penalty Discontinuous Galerkin Finite Element Approximations to the Biharmonic Equation

Igor Mozolevski, Endre Süli and Paulo R. Bösing
Journal of Scientific Computing 30 (3) 465 (2007)
https://doi.org/10.1007/s10915-006-9100-1

ENERGY NORM A POSTERIORI ERROR ESTIMATION OF hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS

PAUL HOUSTON, DOMINIK SCHÖTZAU and THOMAS P. WIHLER
Mathematical Models and Methods in Applied Sciences 17 (01) 33 (2007)
https://doi.org/10.1142/S0218202507001826

hp-version interior penalty DGFEMs for the biharmonic equation

Endre Süli and Igor Mozolevski
Computer Methods in Applied Mechanics and Engineering 196 (13-16) 1851 (2007)
https://doi.org/10.1016/j.cma.2006.06.014

Modular hp-FEM system HERMES and its application to Maxwell’s equations

Tomáš Vejchodský, Pavel Šolín and Martin Zítka
Mathematics and Computers in Simulation 76 (1-3) 223 (2007)
https://doi.org/10.1016/j.matcom.2007.02.001

$hp$-Version Discontinuous Galerkin Finite Element Method for Semilinear Parabolic Problems

Andris Lasis and Endre Süli
SIAM Journal on Numerical Analysis 45 (4) 1544 (2007)
https://doi.org/10.1137/050642125

The Optimal Convergence of theh‐pVersion of the Finite Element Method with Quasi‐Uniform Meshes

Benqi Guo and Weiwei Sun
SIAM Journal on Numerical Analysis 45 (2) 698 (2007)
https://doi.org/10.1137/05063756X

Approximation of acoustic waves by explicit Newmark's schemes and spectral element methods

Elena Zampieri and Luca F. Pavarino
Journal of Computational and Applied Mathematics 185 (2) 308 (2006)
https://doi.org/10.1016/j.cam.2005.03.013

A finite element method using singular functions for Poisson equations: Mixed boundary conditions

Zhiqiang Cai, Seokchan Kim, Sangdong Kim and Sooryun Kong
Computer Methods in Applied Mechanics and Engineering 195 (19-22) 2635 (2006)
https://doi.org/10.1016/j.cma.2005.06.004