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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)
DOI: 10.1142/S0218202507001826
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hp-Version discontinuous Galerkin methods for hyperbolic conservation laws

Kim S. Bey and J. Tinsley Oden
Computer Methods in Applied Mechanics and Engineering 133 (3-4) 259 (1996)
DOI: 10.1016/0045-7825(95)00944-2
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A systematic strategy for simultaneous adaptive hp finite element mesh modification using nonlinear programming

Abani Patra and Ashish Gupta
Computer Methods in Applied Mechanics and Engineering 190 (29-30) 3797 (2001)
DOI: 10.1016/S0045-7825(00)00298-X
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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)
DOI: 10.1137/110844581
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On the Locking of the Finite Element Method in Thermoelasticity

Eric Boillat
SIAM Journal on Numerical Analysis 34 (6) 2319 (1997)
DOI: 10.1137/S0036142996271011
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Finite element solutions for three-dimensional elliptic boundary value problems on unbounded domains

Hae-Soo Oh, Jae-Heon Yun and Bong Soo Jang
Numerical Methods for Partial Differential Equations 22 (6) 1418 (2006)
DOI: 10.1002/num.20151
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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)
DOI: 10.1137/070688006
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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)
DOI: 10.12941/jksiam.2014.18.337
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DIRECT AND INVERSE APPROXIMATION THEOREMS FOR THE p-VERSION OF THE FINITE ELEMENT METHOD IN THE FRAMEWORK OF WEIGHTED BESOV SPACES PART II: OPTIMAL RATE OF CONVERGENCE OF THE p-VERSION FINITE ELEMENT SOLUTIONS

IVO BABUŠKA and BENQI GUO
Mathematical Models and Methods in Applied Sciences 12 (05) 689 (2002)
DOI: 10.1142/S0218202502001854
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On hp- error estimation in the BEM for a three-dimensional Helmholtz exterior problem

Andrzej Karafiat
Computer Methods in Applied Mechanics and Engineering 150 (1-4) 199 (1997)
DOI: 10.1016/S0045-7825(97)00091-1
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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)
DOI: 10.1016/j.aml.2014.05.016
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A Preconditioner Based on Domain Decomposition forh-pFinite-Element Approximation on Quasi-Uniform Meshes

Mark Ainsworth
SIAM Journal on Numerical Analysis 33 (4) 1358 (1996)
DOI: 10.1137/S0036142993258221
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The Convergence of the H-P Version of the Finite Element Method with Quasi-Uniform Meshes for Three Dimensional Poisson Problems with Edge Singularity

Jian Ming Zhang and Yong He
Applied Mechanics and Materials 644-650 1551 (2014)
DOI: 10.4028/www.scientific.net/AMM.644-650.1551
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Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis and Paul Houston
23 (2017)
DOI: 10.1007/978-3-319-67673-9_3
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Finite element analysis of a holonomic elastic-plastic problem

Weimin Han
Numerische Mathematik 60 (1) 493 (1991)
DOI: 10.1007/BF01385733
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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)
DOI: 10.1137/07070423X
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Analysis of a Nonsymmetric Discontinuous Galerkin Method for Elliptic Problems: Stability and Energy Error Estimates

Mats G. Larson and A. Jonas Niklasson
SIAM Journal on Numerical Analysis 42 (1) 252 (2004)
DOI: 10.1137/S0036142902413160
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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)
DOI: 10.1216/JIE-2013-25-1-79
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The Optimalp-Version Approximation of Singularities on Polyhedra in the Boundary Element Method

Christoph Schwab and Manil Suri
SIAM Journal on Numerical Analysis 33 (2) 729 (1996)
DOI: 10.1137/0733037
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Asymptotics of the generalized Gegenbauer functions of fractional degree

Wenjie Liu and Li-Lian Wang
Journal of Approximation Theory 253 105378 (2020)
DOI: 10.1016/j.jat.2020.105378
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hp-version discontinuous Galerkin methods for hyperbolic conservation laws: A parallel adaptive strategy

Kim S. Bey, Abani Patra and J. Tinsley Oden
International Journal for Numerical Methods in Engineering 38 (22) 3889 (1995)
DOI: 10.1002/nme.1620382209
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High-precision quantum algorithms for partial differential equations

Andrew M. Childs, Jin-Peng Liu and Aaron Ostrander
Quantum 5 574 (2021)
DOI: 10.22331/q-2021-11-10-574
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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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P. Houston, B. Senior and E. Süli
631 (2003)
DOI: 10.1007/978-88-470-2089-4_58
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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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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 (3) 543 (2017)
DOI: 10.4208/aamm.2014.m894
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Mixedhp-DGFEM for Incompressible Flows

Dominik Schötzau, Christoph Schwab and Andrea Toselli
SIAM Journal on Numerical Analysis 40 (6) 2171 (2002)
DOI: 10.1137/S0036142901399124
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Families of interior penalty hybridizable discontinuous Galerkin methods for second order elliptic problems

Maurice S. Fabien, Matthew G. Knepley and Beatrice M. Riviere
Journal of Numerical Mathematics 28 (3) 161 (2020)
DOI: 10.1515/jnma-2019-0027
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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)
DOI: 10.1007/s00211-008-0137-y
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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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Error analysis of the spectral element method with Gauss–Lobatto–Legendre points for the acoustic wave equation in heterogeneous media

Saulo Pomponet Oliveira and Stela Angelozi Leite
Applied Numerical Mathematics 129 39 (2018)
DOI: 10.1016/j.apnum.2018.02.007
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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)
DOI: 10.1016/j.cam.2014.01.013
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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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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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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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Equivalence of local- and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H (div)

Alexandre Ern, Thirupathi Gudi, Iain Smears and Martin Vohralík
IMA Journal of Numerical Analysis (2021)
DOI: 10.1093/imanum/draa103
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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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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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Galerkin Method with Discontinuous Basis Functions on Staggered Grips a Priory Estimates for the Homogeneous Dirichlet Problem

R.V. Zhalnin and V.F. Masyagin
Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming and Computer Software" 11 (2) 29 (2018)
DOI: 10.14529/mmp180203
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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)
DOI: 10.1007/s12190-010-0445-0
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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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Quantum algorithms for escaping from saddle points

Chenyi Zhang, Jiaqi Leng and Tongyang Li
Quantum 5 529 (2021)
DOI: 10.22331/q-2021-08-20-529
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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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A discontinuoushp finite element method for the Euler and Navier-Stokes equations

Carlos Erik Baumann and J. Tinsley Oden
International Journal for Numerical Methods in Fluids 31 (1) 79 (1999)
DOI: 10.1002/(SICI)1097-0363(19990915)31:1<79::AID-FLD956>3.0.CO;2-C
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Benchmark computation and performance evaluation for a rhombic plate bending problem

Ivo Babuška and Terenzio Scapolla
International Journal for Numerical Methods in Engineering 28 (1) 155 (1989)
DOI: 10.1002/nme.1620280112
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The p-version of the finite element method for the elliptic boundary value problems with interfaces

Hae-Soo Oh and Ivo Babuška
Computer Methods in Applied Mechanics and Engineering 97 (2) 211 (1992)
DOI: 10.1016/0045-7825(92)90164-F
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Numerical methods and error analysis for one dimensional elliptic problems containing singularities

Hoonjoo Kim, Sung-Jin Lee and Hae-Soo Oh
Numerical Methods for Partial Differential Equations 19 (3) 399 (2003)
DOI: 10.1002/num.10054
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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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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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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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Numerical study of theHP version of mixed discontinuous finite element methods for reaction-diffusion problems: The 1D case

Hongsen Chen, Zhangxin Chen and Baoyan Li
Numerical Methods for Partial Differential Equations 19 (4) 525 (2003)
DOI: 10.1002/num.10063
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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 74 (2) 805 (2018)
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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$hp$-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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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-finite element approximations on non-matching grids for partial differential equations with non-negative characteristic form

Andrea Toselli
ESAIM: Mathematical Modelling and Numerical Analysis 37 (1) 91 (2003)
DOI: 10.1051/m2an:2003018
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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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A posteriori discontinuous Galerkin error estimator for linear elasticity

Robert E. Bird, William M. Coombs and Stefano Giani
Applied Mathematics and Computation 344-345 78 (2019)
DOI: 10.1016/j.amc.2018.08.039
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A first-second order splitting method for a third-order partial differential equation

Q. Duan, G. Li and F. A. Milner
Numerical Methods for Partial Differential Equations 14 (1) 89 (1998)
DOI: 10.1002/(SICI)1098-2426(199801)14:1<89::AID-NUM5>3.0.CO;2-H
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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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Theory and approximation of quasistatic frictional contact problems

C.Y. Lee and J.T. Oden
Computer Methods in Applied Mechanics and Engineering 106 (3) 407 (1993)
DOI: 10.1016/0045-7825(93)90098-I
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A high-order discontinuous Galerkin method for nonlinear sound waves

Paola F. Antonietti, Ilario Mazzieri, Markus Muhr, Vanja Nikolić and Barbara Wohlmuth
Journal of Computational Physics 415 109484 (2020)
DOI: 10.1016/j.jcp.2020.109484
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A Finite Element Method Using Singular Functions for the Poisson Equation: Corner Singularities

Zhiqiang Cai and Seokchan Kim
SIAM Journal on Numerical Analysis 39 (1) 286 (2001)
DOI: 10.1137/S0036142999355945
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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)
DOI: 10.1016/j.amc.2015.01.032
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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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Adaptive virtual element methods with equilibrated fluxes

F. Dassi, J. Gedicke and L. Mascotto
Applied Numerical Mathematics 173 249 (2022)
DOI: 10.1016/j.apnum.2021.11.015
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A posteriori error estimates of hp spectral element methods for integral state constrained elliptic optimal control problems

Yanping Chen, Jinling Zhang, Yunqing Huang and Yeqing Xu
Applied Numerical Mathematics 144 42 (2019)
DOI: 10.1016/j.apnum.2019.05.015
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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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An extension theorem for polynomials on triangles

Norbert Heuer and Florian Leydecker
Calcolo 45 (2) 69 (2008)
DOI: 10.1007/s10092-008-0144-5
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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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hp spectral element approximation for integral state constrained optimal control problems governed by harmonic equations

Yanping Chen, Xiuxiu Lin, Yunqing Huang and Qian Lin
Journal of Computational and Applied Mathematics 371 112716 (2020)
DOI: 10.1016/j.cam.2020.112716
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A scalable exponential-DG approach for nonlinear conservation laws: With application to Burger and Euler equations

Shinhoo Kang and Tan Bui-Thanh
Computer Methods in Applied Mechanics and Engineering 385 114031 (2021)
DOI: 10.1016/j.cma.2021.114031
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Locking effects in the finite element approximation of plate models

Manil Suri, Ivo Babuška and Christoph Schwab
Mathematics of Computation 64 (210) 461 (1995)
DOI: 10.1090/S0025-5718-1995-1277772-6
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The optimal convergence of the h–p version of the boundary element method with quasiuniform meshes for elliptic problems on polygonal domains

Benqi Guo and Norbert Heuer
Advances in Computational Mathematics 24 (1-4) 353 (2006)
DOI: 10.1007/s10444-004-7618-z
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On the stability and convergence of higher-order mixed finite element methods for second-order elliptic problems

Manil Suri
Mathematics of Computation 54 (189) 1 (1990)
DOI: 10.1090/S0025-5718-1990-0990603-X
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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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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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The 𝑝-version of the finite element method for constraint boundary conditions

I. Babuška and Manil Suri
Mathematics of Computation 51 (183) 1 (1988)
DOI: 10.1090/S0025-5718-1988-0942140-7
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Hybrid Discontinuous Galerkin methods with relaxed H(div)-conformity for incompressible flows. Part II

Philip L. Lederer, Christoph Lehrenfeld and Joachim Schöberl
ESAIM: Mathematical Modelling and Numerical Analysis 53 (2) 503 (2019)
DOI: 10.1051/m2an/2018054
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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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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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William F. Mitchell and Marjorie A. McClain
227 (2011)
DOI: 10.1007/978-90-481-9981-5_10
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Formulation of 3D finite elements using curvilinear coordinates

Maria Cinefra
Mechanics of Advanced Materials and Structures 29 (6) 879 (2022)
DOI: 10.1080/15376494.2020.1799122
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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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Less is often more: Applied inverse problems using hp-forward models

Danny Smyl and Dong Liu
Journal of Computational Physics 399 108949 (2019)
DOI: 10.1016/j.jcp.2019.108949
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Lagrange multiplier method with penalty for elliptic and parabolic interface problems

Ajit Patel
Journal of Applied Mathematics and Computing 37 (1-2) 37 (2011)
DOI: 10.1007/s12190-010-0419-2
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$hp$-Version Space-Time Discontinuous Galerkin Methods for Parabolic Problems on Prismatic Meshes

Andrea Cangiani, Zhaonan Dong and Emmanuil H. Georgoulis
SIAM Journal on Scientific Computing 39 (4) A1251 (2017)
DOI: 10.1137/16M1073285
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Paola F. Antonietti, Alberto Ferroni, Ilario Mazzieri and Alfio Quarteroni
119 3 (2017)
DOI: 10.1007/978-3-319-65870-4_1
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Mass Conserving Mixed $hp$-FEM Approximations to Stokes Flow. Part II: Optimal Convergence

Mark Ainsworth and Charles Parker
SIAM Journal on Numerical Analysis 59 (3) 1245 (2021)
DOI: 10.1137/20M1359110
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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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Quality assessment of the a-posteriori error estimation in finite elements

Ivo Babuška, Lothar Plank and Rodolfo Rodríquez
Finite Elements in Analysis and Design 11 (4) 285 (1992)
DOI: 10.1016/0168-874X(92)90011-Z
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Stability Analysis of Polytopic Discontinuous Galerkin Approximations of the Stokes Problem with Applications to Fluid–Structure Interaction Problems

Paola F. Antonietti, Lorenzo Mascotto, Marco Verani and Stefano Zonca
Journal of Scientific Computing 90 (1) (2022)
DOI: 10.1007/s10915-021-01695-6
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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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ℎ𝑝-version discontinuous Galerkin methods on essentially arbitrarily-shaped elements

Andrea Cangiani, Zhaonan Dong and Emmanuil Georgoulis
Mathematics of Computation 91 (333) 1 (2021)
DOI: 10.1090/mcom/3667
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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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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)
DOI: 10.1002/nme.4532
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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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The ultraspherical spectral element method

Daniel Fortunato, Nicholas Hale and Alex Townsend
Journal of Computational Physics 436 110087 (2021)
DOI: 10.1016/j.jcp.2020.110087
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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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Априорные оценки локального разрывного метода Галеркина на разнесенных сетках для решения уравнения параболического типа в рамках однородной задачи Дирихле

Руслан Викторович Жалнин, Ruslan V. Zhalnin, Виктор Федорович Масягин, Victor Fedorovich Masyagin, Елизавета Евгеньевна Пескова, Elizaveta Evgenievna Peskova, Владимир Федорович Тишкин and Vladimir Fedorovich Tishkin
Вестник Самарского государственного технического университета. Серия «Физико-математические науки» 24 (1) 116 (2020)
DOI: 10.14498/vsgtu1747
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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)
DOI: 10.1007/s11425-010-3128-2
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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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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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Toward a universal adaptive finite element strategy, part 2. A posteriori error estimation

J.T. Oden, L. Demkowicz, W. Rachowicz and T.A. Westermann
Computer Methods in Applied Mechanics and Engineering 77 (1-2) 113 (1989)
DOI: 10.1016/0045-7825(89)90130-8
See this article

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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A Block Preconditioner for High-Order Mixed Finite Element Approximations to the Navier--Stokes Equations

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DOI: 10.1137/040609045
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DOI: 10.1016/j.jcp.2017.07.028
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Stabilizedhp-Finite Element Methods for First-Order Hyperbolic Problems

Paul Houston, Christoph Schwab and Endre Süli
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DOI: 10.1137/S0036142998348777
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DOI: 10.1002/num.20259
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Preconditioners for thep-version of the Galerkin method for a coupled finite element/boundary element system

Norbert Heuer and Ernst P. Stephan
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DOI: 10.1002/(SICI)1098-2426(199801)14:1<47::AID-NUM3>3.0.CO;2-L
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Convergence of Discontinuous Galerkin Methods for Incompressible Two-Phase Flow in Heterogeneous Media

Jisheng Kou and Shuyu Sun
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DOI: 10.1137/120898358
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Residual-Based A Posteriori Error Estimates for $hp$-Discontinuous Galerkin Discretizations of the Biharmonic Problem

Zhaonan Dong, Lorenzo Mascotto and Oliver J. Sutton
SIAM Journal on Numerical Analysis 59 (3) 1273 (2021)
DOI: 10.1137/20M1364114
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The p- and hp-versions of the virtual element method for elliptic eigenvalue problems

O. Čertík, F. Gardini, G. Manzini, L. Mascotto and G. Vacca
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DOI: 10.1016/j.camwa.2019.10.018
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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
See this article

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E. Artioli and L. Mascotto
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DOI: 10.1016/j.cma.2021.114024
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Modular hp-FEM system HERMES and its application to Maxwell’s equations

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DOI: 10.1016/j.matcom.2007.02.001
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IMA Journal of Numerical Analysis 38 (4) 1709 (2018)
DOI: 10.1093/imanum/drx062
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Discontinuous Galerkin Approximation of Flows in Fractured Porous Media on Polytopic Grids

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SIAM Journal on Scientific Computing 41 (1) A109 (2019)
DOI: 10.1137/17M1138194
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ℎ𝑝-Discontinuous Galerkin methods for the Helmholtz equation with large wave number

Xiaobing Feng and Haijun Wu
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DOI: 10.1090/S0025-5718-2011-02475-0
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Discontinuous Galerkin methods for simulating bioreactive transport of viruses in porous media

Shuyu Sun and Mary F. Wheeler
Advances in Water Resources 30 (6-7) 1696 (2007)
DOI: 10.1016/j.advwatres.2006.05.033
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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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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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hp-Adaptive Discontinuous Galerkin Finite Element Methods for First-Order Hyperbolic Problems

Paul Houston and Endre Süli
SIAM Journal on Scientific Computing 23 (4) 1226 (2001)
DOI: 10.1137/S1064827500378799
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A stable Petrov-Galerkin method for convection-dominated problems

Regina C. Almeida and Renato S. Silva
Computer Methods in Applied Mechanics and Engineering 140 (3-4) 291 (1997)
DOI: 10.1016/S0045-7825(96)01108-5
See this article

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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A stable mixed finite element method for nearly incompressible linear elastostatics

Eirik Valseth, Albert Romkes, Austin R. Kaul and Clint Dawson
International Journal for Numerical Methods in Engineering 122 (17) 4709 (2021)
DOI: 10.1002/nme.6743
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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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Locking effects in the finite element approximation of elasticity problems

Ivo Babuška and Manil Suri
Numerische Mathematik 62 (1) 439 (1992)
DOI: 10.1007/BF01396238
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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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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)
DOI: 10.1016/j.cma.2010.08.003
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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)
DOI: 10.1016/j.cam.2013.09.053
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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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High-order polygonal discontinuous Petrov–Galerkin (PolyDPG) methods using ultraweak formulations

Ali Vaziri Astaneh, Federico Fuentes, Jaime Mora and Leszek Demkowicz
Computer Methods in Applied Mechanics and Engineering 332 686 (2018)
DOI: 10.1016/j.cma.2017.12.011
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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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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
See this article

Nodal High-Order Methods on Unstructured Grids

J.S Hesthaven and T Warburton
Journal of Computational Physics 181 (1) 186 (2002)
DOI: 10.1006/jcph.2002.7118
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New Development of the P and H-P Version Finite Element Method with Quasi-Uniform Meshes for Elliptic Problems

Jian Ming Zhang and Yong He
Applied Mechanics and Materials 444-445 671 (2013)
DOI: 10.4028/www.scientific.net/AMM.444-445.671
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A Priori Error Estimates for Finite Element Methods Based on Discontinuous Approximation Spaces for Elliptic Problems

Béatrice Rivière, Mary F. Wheeler and Vivette Girault
SIAM Journal on Numerical Analysis 39 (3) 902 (2001)
DOI: 10.1137/S003614290037174X
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ERROR ESTIMATES OF SEMIDISCRETE DISCONTINUOUS GALERKIN APPROXIMATIONS FOR THE VISCOELASTICITY-TYPE EQUATION

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Bulletin of the Korean Mathematical Society 49 (4) 829 (2012)
DOI: 10.4134/BKMS.2012.49.4.829
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Toward a universal adaptive finite element strategy, part 1. Constrained approximation and data structure

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Computer Methods in Applied Mechanics and Engineering 77 (1-2) 79 (1989)
DOI: 10.1016/0045-7825(89)90129-1
See this article

Endre Süli, Paul Houston and Christoph Schwab
143 (2000)
DOI: 10.1016/B978-008043568-8/50008-0
See this article

Toward a universal adaptive finite element strategy part 3. design of meshes

W. Rachowicz, J.T. Oden and L. Demkowicz
Computer Methods in Applied Mechanics and Engineering 77 (1-2) 181 (1989)
DOI: 10.1016/0045-7825(89)90131-X
See this article

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

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Mathematical Models and Methods in Applied Sciences 23 (05) 777 (2013)
DOI: 10.1142/S0218202512500601
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High order discontinuous Galerkin method for reduced flow models in fractured porous media

Igor Mozolevski, Marcio A. Murad and Luciane A. Schuh
Mathematics and Computers in Simulation 190 1317 (2021)
DOI: 10.1016/j.matcom.2021.07.012
See this article

On the convergence rate of the cell discretization algorithm for solving elliptic problems

Maria Cayco, Leslie Foster and Howard Swann
Mathematics of Computation 64 (212) 1397 (1995)
DOI: 10.1090/S0025-5718-1995-1297464-7
See this article

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
See this article

Anisotropic hp-mesh optimization technique based on the continuous mesh and error models

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Computers & Mathematics with Applications 74 (1) 45 (2017)
DOI: 10.1016/j.camwa.2016.12.015
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Theh-p version of the finite element method for problems with interfaces

Benqi Guo and Hae-Soo Oh
International Journal for Numerical Methods in Engineering 37 (10) 1741 (1994)
DOI: 10.1002/nme.1620371007
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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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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)
DOI: 10.1007/s10915-009-9281-5
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A stable space-time FE method for the shallow water equations

Eirik Valseth and Clint Dawson
Computational Geosciences 26 (1) 53 (2022)
DOI: 10.1007/s10596-021-10108-4
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An adaptive high-order unfitted finite element method for elliptic interface problems

Zhiming Chen, Ke Li and Xueshuang Xiang
Numerische Mathematik 149 (3) 507 (2021)
DOI: 10.1007/s00211-021-01243-2
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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)
DOI: 10.1137/080722953
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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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An unconditionally stable space–time FE method for the Korteweg–de Vries equation

Eirik Valseth and Clint Dawson
Computer Methods in Applied Mechanics and Engineering 371 113297 (2020)
DOI: 10.1016/j.cma.2020.113297
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A unified algorithm for the selection of collocation stencils for convex, concave, and singular problems

Thibault Jacquemin and Stéphane P. A. Bordas
International Journal for Numerical Methods in Engineering 122 (16) 4292 (2021)
DOI: 10.1002/nme.6703
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A posteriori error estimation and dynamic adaptivity for symmetric discontinuous Galerkin approximations of reactive transport problems

Shuyu Sun and Mary F. Wheeler
Computer Methods in Applied Mechanics and Engineering 195 (7-8) 632 (2006)
DOI: 10.1016/j.cma.2005.02.021
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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)
DOI: 10.2478/s11600-014-0212-y
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Stabilized spectral element approximation for the Navier-Stokes equations

P. Gervasio and F. Saleri
Numerical Methods for Partial Differential Equations 14 (1) 115 (1998)
DOI: 10.1002/(SICI)1098-2426(199801)14:1<115::AID-NUM7>3.0.CO;2-T
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The p- and h-p versions of the finite element method, an overview

Ivo Babuška and Manil Suri
Computer Methods in Applied Mechanics and Engineering 80 (1-3) 5 (1990)
DOI: 10.1016/0045-7825(90)90011-A
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On the convergence of the 𝑝-version of the boundary element Galerkin method

E. P. Stephan and M. Suri
Mathematics of Computation 52 (185) 31 (1989)
DOI: 10.1090/S0025-5718-1989-0947469-5
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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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Locking-Free Enriched Galerkin Method for Linear Elasticity

Son-Young Yi, Sanghyun Lee and Ludmil Zikatanov
SIAM Journal on Numerical Analysis 60 (1) 52 (2022)
DOI: 10.1137/21M1391353
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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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An explicit second order spectral element method for acoustic waves

Elena Zampieri and Luca F. Pavarino
Advances in Computational Mathematics 25 (4) 381 (2006)
DOI: 10.1007/s10444-004-7626-z
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