ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN)

Polynomial Extension Operators. Part I

Leszek Demkowicz, Jayadeep Gopalakrishnan and Joachim Schöberl
SIAM Journal on Numerical Analysis 46 (6) 3006 (2008)
DOI: 10.1137/070698786
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Implementation of nonhomogeneous dirichlet boundary conditions in the p version of the finite element method

Ivo Babušjka, B. Guoz and Manil Suri
IMPACT of Computing in Science and Engineering 1 (1) 36 (1989)
DOI: 10.1016/0899-8248(89)90019-0
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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)
DOI: 10.1016/j.cam.2008.08.026
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Discontinuous Galerkin methods for coupled flow and reactive transport problems

Shuyu Sun and Mary F. Wheeler
Applied Numerical Mathematics 52 (2-3) 273 (2005)
DOI: 10.1016/j.apnum.2004.08.035
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A Trefftz Polynomial Space-Time Discontinuous Galerkin Method for the Second Order Wave Equation

Lehel Banjai, Emmanuil H. Georgoulis and Oluwaseun Lijoka
SIAM Journal on Numerical Analysis 55 (1) 63 (2017)
DOI: 10.1137/16M1065744
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Construction and Analysis of HDG Methods for Linearized Shallow Water Equations

Tan Bui-Thanh
SIAM Journal on Scientific Computing 38 (6) A3696 (2016)
DOI: 10.1137/16M1057243
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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)
DOI: 10.1016/j.cam.2012.01.025
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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)
DOI: 10.1007/s13226-015-0160-5
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Local high-order regularization and applications to hp-methods

M. Karkulik and J.M. Melenk
Computers & Mathematics with Applications 70 (7) 1606 (2015)
DOI: 10.1016/j.camwa.2015.06.026
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Superconvergence Analysis of Gradient Recovery Method for TM Model of Electromagnetic Scattering in the Cavity

Shanghui Jia, Changhui Yao and Hehu Xie
Advances in Applied Mathematics and Mechanics 9 (03) 543 (2017)
DOI: 10.4208/aamm.2014.m894
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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)
DOI: 10.1016/j.amc.2007.10.053
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The h, p and h-p version of the finite element method; basis theory and applications

I. Babuška and B.Q. Guo
Advances in Engineering Software 15 (3-4) 159 (1992)
DOI: 10.1016/0965-9978(92)90097-Y
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A Block Preconditioner for High-Order Mixed Finite Element Approximations to the Navier--Stokes Equations

David Kay and Emil Lungu
SIAM Journal on Scientific Computing 27 (6) 1867 (2006)
DOI: 10.1137/040609045
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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)
DOI: 10.4134/BKMS.2012.49.4.829
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The Mathematics of Finite Elements and Applications X

Endre Süli, Paul Houston and Christoph Schwab
The Mathematics of Finite Elements and Applications X 143 (2000)
DOI: 10.1016/B978-008043568-8/50008-0
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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)
DOI: 10.1142/S0218202512500601
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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)
DOI: 10.1137/120888405
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On the coupling of local multilevel mesh refinement and ZZ methods for unilateral frictional contact problems in elastostatics

H. Liu, I. Ramière and F. Lebon
Computer Methods in Applied Mechanics and Engineering 323 1 (2017)
DOI: 10.1016/j.cma.2017.04.011
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HP DISCONTINUOUS GALERKIN APPROXIMATIONS FOR THE STOKES PROBLEM

ANDREA TOSELLI
Mathematical Models and Methods in Applied Sciences 12 (11) 1565 (2002)
DOI: 10.1142/S0218202502002240
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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)
DOI: 10.1016/j.cam.2005.11.021
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The p and hp finite element method for problems on thin domains

Manil Suri
Journal of Computational and Applied Mathematics 128 (1-2) 235 (2001)
DOI: 10.1016/S0377-0427(00)00514-8
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Stabilizedhp-Finite Element Methods for First-Order Hyperbolic Problems

Paul Houston, Christoph Schwab and Endre Süli
SIAM Journal on Numerical Analysis 37 (5) 1618 (2000)
DOI: 10.1137/S0036142998348777
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Analysis of an interior penalty discontinuous Galerkin scheme for two phase flow in porous media with dynamic capillary effects

Stefan Karpinski and Iuliu Sorin Pop
Numerische Mathematik 136 (1) 249 (2017)
DOI: 10.1007/s00211-016-0839-5
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The $h-p$ version of the boundary element method on polygonal domains with quasiuniform meshes

E. P. Stephan and M. Suri
ESAIM: Mathematical Modelling and Numerical Analysis 25 (6) 783 (1991)
DOI: 10.1051/m2an/1991250607831
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hp-adaptive extended finite element method

A. Byfut and A. Schröder
International Journal for Numerical Methods in Engineering 89 (11) 1392 (2012)
DOI: 10.1002/nme.3293
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Anisotropic h p -mesh optimization technique based on the continuous mesh and error models

Vít Dolejší, Georg May, Filip Roskovec and Pavel Solin
Computers & Mathematics with Applications 74 (1) 45 (2017)
DOI: 10.1016/j.camwa.2016.12.015
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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)
DOI: 10.1016/j.cam.2005.03.013
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A multi-level refinement adaptive scheme with high efficiency and accuracy

Chensen Ding, Xiangyang Cui, Chong Li, Guangyao Li and Guoping Wang
Engineering Computations 33 (7) 2216 (2016)
DOI: 10.1108/EC-05-2015-0119
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An adaptive refinement strategy for hp-finite element computations

Mark Ainsworth and Bill Senior
Applied Numerical Mathematics 26 (1-2) 165 (1998)
DOI: 10.1016/S0168-9274(97)00083-4
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Relèvement polynômial de traces et applications

Christine Bernardi and Yvon Maday
ESAIM: Mathematical Modelling and Numerical Analysis 24 (5) 557 (1990)
DOI: 10.1051/m2an/1990240505571
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$hp$-Adaptation Driven by Polynomial-Degree-Robust A Posteriori Error Estimates for Elliptic Problems

Vít Dolejší, Alexandre Ern and Martin Vohralík
SIAM Journal on Scientific Computing 38 (5) A3220 (2016)
DOI: 10.1137/15M1026687
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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)
DOI: 10.1016/j.cam.2011.02.004
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Hodge Decomposition Methods for a Quad-Curl Problem on Planar Domains

Susanne C. Brenner, Jiguang Sun and Li-yeng Sung
Journal of Scientific Computing (2017)
DOI: 10.1007/s10915-017-0449-0
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A discontinuous hp finite element method for diffusion problems: 1-D analysis

I. Babuška, C.E. Baumann and J.T. Oden
Computers & Mathematics with Applications 37 (9) 103 (1999)
DOI: 10.1016/S0898-1221(99)00117-0
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Analysis of Discontinuous Galerkin Methods for Multicomponent Reactive Transport Problems

Shuyu Sun and M.F. Wheeler
Computers & Mathematics with Applications 52 (5) 637 (2006)
DOI: 10.1016/j.camwa.2006.10.004
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An Unfitted Discontinuous Galerkin Method Applied to Elliptic Interface Problems

Ralf Massjung
SIAM Journal on Numerical Analysis 50 (6) 3134 (2012)
DOI: 10.1137/090763093
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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)
DOI: 10.1137/120898358
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A collection of 2D elliptic problems for testing adaptive grid refinement algorithms

William F. Mitchell
Applied Mathematics and Computation 220 350 (2013)
DOI: 10.1016/j.amc.2013.05.068
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Staggered grids hybrid-dual spectral element method for second-order elliptic problems application to high-order time splitting methods for Navier-Stokes equations

M. Azaïez, F.Ben Belgacem, M. Grundmann and H. Khallouf
Computer Methods in Applied Mechanics and Engineering 166 (3-4) 183 (1998)
DOI: 10.1016/S0045-7825(98)00069-3
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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)
DOI: 10.1186/s13660-016-0994-3
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Information-based numerical practice

I Babuška
Journal of Complexity 3 (3) 331 (1987)
DOI: 10.1016/0885-064X(87)90019-7
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A priori error estimation of hp-finite element approximations of frictional contact problems with normal compliance

C.Y. Lee and J.Tinsley Oden
International Journal of Engineering Science 31 (6) 927 (1993)
DOI: 10.1016/0020-7225(93)90104-3
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Analysis of the Efficiency of an a Posteriori Error Estimator for Linear Triangular Finite Elements

Ivo Babuška, Ricardo Durán and Rodolfo Rodríguez
SIAM Journal on Numerical Analysis 29 (4) 947 (1992)
DOI: 10.1137/0729058
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Analytic regularity of Stokes flow on polygonal domains in countably weighted Sobolev spaces

Benqi Guo and Christoph Schwab
Journal of Computational and Applied Mathematics 190 (1-2) 487 (2006)
DOI: 10.1016/j.cam.2005.02.018
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Mixed Finite Element Methods of Higher-Order for Model Contact Problems

Andreas Schröder
SIAM Journal on Numerical Analysis 49 (6) 2323 (2011)
DOI: 10.1137/090770072
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$hp$-Version Discontinuous Galerkin Finite Element Method for Semilinear Parabolic Problems

Andris Lasis and Endre Süli
SIAM Journal on Numerical Analysis 45 (4) 1544 (2007)
DOI: 10.1137/050642125
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Efficient Preconditioning for thep-Version Finite Element Method in Two Dimensions

I. Babuška, A. Craig, J. Mandel and J. Pitkäranta
SIAM Journal on Numerical Analysis 28 (3) 624 (1991)
DOI: 10.1137/0728034
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Finite Elements for Elliptic Problems with Highly Varying, Nonperiodic Diffusion Matrix

D. Peterseim and S. Sauter
Multiscale Modeling & Simulation 10 (3) 665 (2012)
DOI: 10.1137/10081839X
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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)
DOI: 10.1016/j.matcom.2007.02.001
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Stability and convergence of nonconforming hp finite-element methods

P. Seshaiyer
Computers & Mathematics with Applications 46 (1) 165 (2003)
DOI: 10.1016/S0898-1221(03)90087-3
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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)
DOI: 10.1016/j.apnum.2011.06.015
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An engineering application of the h-p Version of the finite element method to the static analysis of a Euler-Bernoulli beam

N.S. Bardell
Computers & Structures 59 (2) 195 (1996)
DOI: 10.1016/0045-7949(95)00252-9
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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)
DOI: 10.1137/110828010
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An hp-Hybrid High-Order Method for Variable Diffusion on General Meshes

Joubine Aghili, Daniele A. Di Pietro and Berardo Ruffini
Computational Methods in Applied Mathematics 17 (3) (2017)
DOI: 10.1515/cmam-2017-0009
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Dynamically adapted mesh refinement for combustion front tracking

Pierre Haldenwang and Didier Pignol
Computers & Fluids 31 (4-7) 589 (2002)
DOI: 10.1016/S0045-7930(01)00064-0
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A Priori error analyses of a stabilized discontinuous Galerkin method

A. Romkes, S. Prudhomme and J.T. Oden
Computers & Mathematics with Applications 46 (8-9) 1289 (2003)
DOI: 10.1016/S0898-1221(03)90220-3
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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)
DOI: 10.1016/j.cam.2007.10.055
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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)
DOI: 10.1137/120874643
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Numerical simulation of resistivity LWD tool based on higher-order vector finite element

Li Hui, Shen Yi-ze and Zhu Xi-fang
Journal of Petroleum Exploration and Production Technology 6 (3) 533 (2016)
DOI: 10.1007/s13202-015-0200-z
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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)
DOI: 10.1016/j.jcp.2012.01.037
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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 (02) 163 (2013)
DOI: 10.4208/aamm.11-m1140
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On Locking and Robustness in the Finite Element Method

Ivo Babuška and Manil Suri
SIAM Journal on Numerical Analysis 29 (5) 1261 (1992)
DOI: 10.1137/0729075
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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)
DOI: 10.1137/050643362
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Analysis of a semidiscrete discontinuous Galerkin scheme for compressible miscible displacement problem

Mingrong Cui
Journal of Computational and Applied Mathematics 214 (2) 617 (2008)
DOI: 10.1016/j.cam.2007.03.019
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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)
DOI: 10.1137/090747208
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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)
DOI: 10.1016/j.jmaa.2012.08.033
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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)
DOI: 10.1007/s00791-012-0179-7
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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)
DOI: 10.1137/110854898
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Additive Schwarz algorithms for solving hp-version finite element systems on triangular meshes

V. Korneev, J.E. Flaherty, J.T. Oden and J. Fish
Applied Numerical Mathematics 43 (4) 399 (2002)
DOI: 10.1016/S0168-9274(02)00104-6
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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)
DOI: 10.1007/s13160-012-0096-7
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Residual-based a posteriori error estimates for hp finite element solutions of semilinear Neumann boundary optimal control problems

Zuliang Lu, Shuhua Zhang, Chuanjuan Hou and Hongyan Liu
Boundary Value Problems 2016 (1) (2016)
DOI: 10.1186/s13661-016-0562-2
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On a nonoverlapping additive Schwarz method forh-pdiscontinuous Galerkin discretization of elliptic problems

Piotr Krzyżanowski
Numerical Methods for Partial Differential Equations 32 (6) 1572 (2016)
DOI: 10.1002/num.22063
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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)
DOI: 10.1016/j.cam.2008.08.036
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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)
DOI: 10.1016/j.cma.2011.11.004
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Construction of polynomial extensions in two dimensions and application to the finite element method

Benqi Guo and Jianming Zhang
Journal of Computational and Applied Mathematics 261 249 (2014)
DOI: 10.1016/j.cam.2013.09.053
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Mixed finite element methods for nonlinear elliptic problems: the h-p version

Miyoung Lee and Fabio A. Milner
Journal of Computational and Applied Mathematics 85 (2) 239 (1997)
DOI: 10.1016/S0377-0427(97)00121-0
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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)
DOI: 10.1137/090753802
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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)
DOI: 10.1137/070701066
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Parallel Domain Decomposition Solver for Adaptive hp Finite Element Methods

J. T. Oden, Abani Patra and Yusheng Feng
SIAM Journal on Numerical Analysis 34 (6) 2090 (1997)
DOI: 10.1137/S0036142994278887
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Discontinuous hp-Finite Element Methods for Advection-Diffusion-Reaction Problems

Paul Houston, Christoph Schwab and Endre Süli
SIAM Journal on Numerical Analysis 39 (6) 2133 (2002)
DOI: 10.1137/S0036142900374111
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Basic principles of hp virtual elements on quasiuniform meshes

L. Beir ao da Veiga, A. Chernov, L. Mascotto and A. Russo
Mathematical Models and Methods in Applied Sciences 26 (08) 1567 (2016)
DOI: 10.1142/S021820251650038X
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Distributed Lagrange Multiplier Functions for Fictitious Domain Method with Spectral/hp Element Discretization

Riccardo Zamolo, Lucia Parussini and Valentino Pediroda
Journal of Scientific Computing (2017)
DOI: 10.1007/s10915-017-0464-1
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A parallel hp-adaptive discontinuous Galerkin method for hyperbolic conservation laws

Kim S. Bey, J. Tinsley Oden and Abani Patra
Applied Numerical Mathematics 20 (4) 321 (1996)
DOI: 10.1016/0168-9274(95)00101-8
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Partial Differential Equations

Manil Suri
Partial Differential Equations 235 (2001)
DOI: 10.1016/B978-0-444-50616-0.50010-5
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Thepandh-pVersions of the Finite Element Method, Basic Principles and Properties

Ivo Babuška and Manil Suri
SIAM Review 36 (4) 578 (1994)
DOI: 10.1137/1036141
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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)
DOI: 10.1142/S0218202514500146
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$hp$-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)
DOI: 10.1137/120877246
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Error analysis of a coupled finite–infinite element method for an exterior Poisson problem

Chunxiong Zheng
Applied Numerical Mathematics 57 (3) 270 (2007)
DOI: 10.1016/j.apnum.2006.03.010
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The $h-p$ version of the finite element method with quasiuniform meshes

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