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:

A Review of Numerical Techniques for Frictional Contact Analysis

Govind Vashishtha, Sumika Chauhan, Riya Singh, Manpreet Singh and Ghanshyam G. Tejani
Lubricants 13 (1) 18 (2025)
https://doi.org/10.3390/lubricants13010018

hp-optimal convergence of the original DG method for linear hyperbolic problems on special simplicial meshes

Z Dong and L Mascotto
IMA Journal of Numerical Analysis 45 (3) 1372 (2025)
https://doi.org/10.1093/imanum/drae051

The multigrid discretization of mixed discontinuous Galerkin method for the biharmonic eigenvalue problem

Jinhua Feng, Shixi Wang, Hai Bi and Yidu Yang
Mathematical Methods in the Applied Sciences 48 (2) 2635 (2025)
https://doi.org/10.1002/mma.10455

An hp-Adaptive Strategy Based on Locally Predicted Error Reductions

Patrick Bammer, Andreas Schröder and Thomas P. Wihler
Computational Methods in Applied Mathematics (2025)
https://doi.org/10.1515/cmam-2023-0250

Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport

Paul Houston, Matthew E. Hubbard, Thomas J. Radley, Oliver J. Sutton and Richard S. J. Widdowson
Journal of Scientific Computing 100 (2) (2024)
https://doi.org/10.1007/s10915-024-02569-3

Enhanced and efficient scaled boundary finite elements for mechanical problems under the action of body loads

Karolinne O. Coelho, Philippe R.B. Devloo and Sônia M. Gomes
Computer Methods in Applied Mechanics and Engineering 420 116695 (2024)
https://doi.org/10.1016/j.cma.2023.116695

A stable local commuting projector and optimal hp approximation estimates in $$\varvec{H}(\textrm{curl})$$

Théophile Chaumont-Frelet and Martin Vohralík
Numerische Mathematik 156 (6) 2293 (2024)
https://doi.org/10.1007/s00211-024-01431-w

A parameter-free and locking-free enriched Galerkin method of arbitrary order for linear elasticity

Shuai Su, Siyuan Tong, Mingyan Zhang and Qian Zhang
Computer Methods in Applied Mechanics and Engineering 432 117375 (2024)
https://doi.org/10.1016/j.cma.2024.117375

A priori and a posteriori error analysis of hp spectral element discretization for optimal control problems with elliptic equations

Xiuxiu Lin, Yanping Chen and Yunqing Huang
Journal of Computational and Applied Mathematics 423 114960 (2023)
https://doi.org/10.1016/j.cam.2022.114960

A two‐grid discontinuous Galerkin method for an incompressible miscible displacement problem

Jiming Yang, Jing Zhou and Yifan Su
Numerical Methods for Partial Differential Equations 39 (4) 2763 (2023)
https://doi.org/10.1002/num.22986

Pricing Multiasset Derivatives by Variational Quantum Algorithms

Kenji Kubo, Koichi Miyamoto, Kosuke Mitarai and Keisuke Fujii
IEEE Transactions on Quantum Engineering 4 1 (2023)
https://doi.org/10.1109/TQE.2023.3269525

An arbitrarily high order unfitted finite element method for elliptic interface problems with automatic mesh generation

Zhiming Chen and Yong Liu
Journal of Computational Physics 491 112384 (2023)
https://doi.org/10.1016/j.jcp.2023.112384

A simple equilibration procedure leading to polynomial-degree-robust a posteriori error estimators for the curl-curl problem

T. Chaumont-Frelet
Mathematics of Computation 92 (344) 2413 (2023)
https://doi.org/10.1090/mcom/3817

Analysis of a full-discrete two-grid discontinuous Galerkin method for nonlinear parabolic equations

Jiming Yang, Jing Zhou and Hongbin Chen
Computational and Applied Mathematics 42 (4) (2023)
https://doi.org/10.1007/s40314-023-02297-8

An hp-mixed discontinuous Galerkin method for the biharmonic eigenvalue problem

Jinhua Feng, Shixi Wang, Hai Bi and Yidu Yang
Applied Mathematics and Computation 450 127969 (2023)
https://doi.org/10.1016/j.amc.2023.127969

Penalty-Free Any-Order Weak Galerkin FEMs for Linear Elasticity on Quadrilateral Meshes

Ruishu Wang, Zhuoran Wang and Jiangguo Liu
Journal of Scientific Computing 95 (1) (2023)
https://doi.org/10.1007/s10915-023-02151-3

An hp error analysis of a hybrid discontinuous mixed Galerkin method for linear viscoelasticity

Salim Meddahi
Computer Methods in Applied Mechanics and Engineering 417 116452 (2023)
https://doi.org/10.1016/j.cma.2023.116452

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)
https://doi.org/10.1007/s10915-021-01695-6

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 42 (2) 1023 (2022)
https://doi.org/10.1093/imanum/draa103

Unlocking the secrets of locking: Finite element analysis in planar linear elasticity

Mark Ainsworth and Charles Parker
Computer Methods in Applied Mechanics and Engineering 395 115034 (2022)
https://doi.org/10.1016/j.cma.2022.115034

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)
https://doi.org/10.1137/21M1391353

Residual-based a posteriori error estimates for the hp version of the finite element discretization of the elliptic Robin boundary control problem

Samuel Gbéya, Koffi Wilfrid Houédanou, Lewis Nyaga and Bernardin Ahounou
Results in Applied Mathematics 14 100278 (2022)
https://doi.org/10.1016/j.rinam.2022.100278

An MsFEM Approach Enriched Using Legendre Polynomials

Frédéric Legoll, Pierre-Loïk Rothé, Claude Le Bris and Ulrich Hetmaniuk
Multiscale Modeling & Simulation 20 (2) 798 (2022)
https://doi.org/10.1137/21M1444151

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)
https://doi.org/10.1137/20M1359110

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)
https://doi.org/10.1137/20M1364114

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)
https://doi.org/10.1016/j.cma.2021.114031

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)
https://doi.org/10.1007/s00211-021-01243-2

ℎ𝑝-version discontinuous Galerkin methods on essentially arbitrarily-shaped elements

Andrea Cangiani, Zhaonan Dong and Emmanuil Georgoulis
Mathematics of Computation 91 (333) 1 (2021)
https://doi.org/10.1090/mcom/3667

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)
https://doi.org/10.1002/nme.6743

Enrichment of the nonconforming virtual element method with singular functions

E. Artioli and L. Mascotto
Computer Methods in Applied Mechanics and Engineering 385 114024 (2021)
https://doi.org/10.1016/j.cma.2021.114024

Error estimates for the Scaled Boundary Finite Element Method

Karolinne O. Coelho, Philippe R.B. Devloo and Sônia M. Gomes
Computer Methods in Applied Mechanics and Engineering 379 113765 (2021)
https://doi.org/10.1016/j.cma.2021.113765

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)
https://doi.org/10.1002/nme.6703

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)
https://doi.org/10.1016/j.matcom.2021.07.012

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)
https://doi.org/10.1016/j.cma.2020.113297

Априорные оценки локального разрывного метода Галеркина на разнесенных сетках для решения уравнения параболического типа в рамках однородной задачи Дирихле

Ruslan V. Zhalnin, Руслан Викторович Жалнин, Виктор Федорович Масягин, et al.
Вестник Самарского государственного технического университета. Серия «Физико-математические науки» 24 (1) 116 (2020)
https://doi.org/10.14498/vsgtu1747

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)
https://doi.org/10.1016/j.jcp.2020.109484

Convergence analysis of an energy based discontinuous Galerkin method for the wave equation in second-order form: hp version

Yu Du and Jiangxing Wang
Computers & Mathematics with Applications 79 (11) 3223 (2020)
https://doi.org/10.1016/j.camwa.2020.01.017

A posteriori error estimates of hp spectral element methods for optimal control problems with L2-norm state constraint

Xiuxiu Lin, Yanping Chen and Yunqing Huang
Numerical Algorithms 83 (3) 1145 (2020)
https://doi.org/10.1007/s11075-019-00719-5

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
Computers & Mathematics with Applications 79 (7) 2035 (2020)
https://doi.org/10.1016/j.camwa.2019.10.018

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)
https://doi.org/10.1016/j.cam.2020.112716

$H^2$-Stable Polynomial Liftings on Triangles

Mark Ainsworth and Charles Parker
SIAM Journal on Numerical Analysis 58 (3) 1867 (2020)
https://doi.org/10.1137/19M128171X

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)
https://doi.org/10.1515/jnma-2019-0027

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)
https://doi.org/10.1016/j.apnum.2019.05.015

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)
https://doi.org/10.1016/j.amc.2018.08.039

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)
https://doi.org/10.1051/m2an/2018054

A Discontinuous Galerkin Finite Element Method fOR Uniformly Elliptic Two Dimensional Oblique Boundary-Value Problems

Ellya L. Kawecki
SIAM Journal on Numerical Analysis 57 (2) 751 (2019)
https://doi.org/10.1137/17M1155946

Discontinuous Galerkin Approximation of Flows in Fractured Porous Media on Polytopic Grids

Paola F. Antonietti, Chiara Facciolà, Alessandro Russo and Marco Verani
SIAM Journal on Scientific Computing 41 (1) A109 (2019)
https://doi.org/10.1137/17M1138194

Exponential convergence of the hp virtual element method in presence of corner singularities

L. Beirão da Veiga, A. Chernov, L. Mascotto and A. Russo
Numerische Mathematik 138 (3) 581 (2018)
https://doi.org/10.1007/s00211-017-0921-7

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)
https://doi.org/10.14529/mmp180203

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)
https://doi.org/10.1016/j.apnum.2018.02.007

Polynomial robust stability analysis for $H$(div)-conforming finite elements for the Stokes equations

Philip L Lederer and Joachim Schöberl
IMA Journal of Numerical Analysis 38 (4) 1832 (2018)
https://doi.org/10.1093/imanum/drx051

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)
https://doi.org/10.1016/j.cma.2017.12.011

$C^0$ Interior Penalty Methods for an Elliptic Distributed Optimal Control Problem on Nonconvex Polygonal Domains with Pointwise State Constraints

Susanne C. Brenner, Joscha Gedicke and Li-yeng Sung
SIAM Journal on Numerical Analysis 56 (3) 1758 (2018)
https://doi.org/10.1137/17M1140649

Predictor–corrector p- and hp-versions of the finite element method for Poisson’s equation in polygonal domains

B. Nkemzi and S. Tanekou
Computer Methods in Applied Mechanics and Engineering 333 74 (2018)
https://doi.org/10.1016/j.cma.2018.01.027

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)
https://doi.org/10.1007/s10915-017-0464-1

A priori and a posteriori error control of discontinuous Galerkin finite element methods for the von Kármán equations

Carsten Carstensen, Gouranga Mallik and Neela Nataraj
IMA Journal of Numerical Analysis (2018)
https://doi.org/10.1093/imanum/dry003

A high-order discontinuous Galerkin approximation to ordinary differential equations with applications to elastodynamics

Paola F Antonietti, Ilario Mazzieri, Niccolò Dal Santo and Alfio Quarteroni
IMA Journal of Numerical Analysis 38 (4) 1709 (2018)
https://doi.org/10.1093/imanum/drx062

A priori error estimates of a combined mixed finite element and local discontinuous Galerkin method for an incompressible miscible displacement problem

Jiming Yang, Yanping Chen and Yunqing Huang
Applied Mathematics and Computation 334 141 (2018)
https://doi.org/10.1016/j.amc.2017.12.022

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016

Paola F. Antonietti, Alberto Ferroni, Ilario Mazzieri and Alfio Quarteroni
Lecture Notes in Computational Science and Engineering, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016 119 3 (2017)
https://doi.org/10.1007/978-3-319-65870-4_1

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)
https://doi.org/10.4208/aamm.2014.m894

Anisotropic hp-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)
https://doi.org/10.1016/j.camwa.2016.12.015

Superconvergence Analysis of Gradient Recovery Method for TM Model of Electromagnetic Scattering in the Cavity

Shanghui Jia and Changhui Yao
Advances in Applied Mathematics and Mechanics 9 (5) 1133 (2017)
https://doi.org/10.4208/aamm.2015.m1136

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) 359 (2017)
https://doi.org/10.1515/cmam-2017-0009

Hodge Decomposition Methods for a Quad-Curl Problem on Planar Domains

Susanne C. Brenner, Jiguang Sun and Li-yeng Sung
Journal of Scientific Computing 73 (2-3) 495 (2017)
https://doi.org/10.1007/s10915-017-0449-0

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)
https://doi.org/10.1016/j.cma.2017.04.011

hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes

Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis and Paul Houston
SpringerBriefs in Mathematics, hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes 23 (2017)
https://doi.org/10.1007/978-3-319-67673-9_3

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)
https://doi.org/10.1137/16M1065744

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)
https://doi.org/10.1007/s00211-016-0839-5

$hp$-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)
https://doi.org/10.1137/16M1073285

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)
https://doi.org/10.1007/s13202-015-0200-z

On a nonoverlapping additive Schwarz method for h‐p discontinuous Galerkin discretization of elliptic problems

Piotr Krzyżanowski
Numerical Methods for Partial Differential Equations 32 (6) 1572 (2016)
https://doi.org/10.1002/num.22063

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

$hp$-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)
https://doi.org/10.1137/15M1026687

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)
https://doi.org/10.1108/EC-05-2015-0119

Construction and Analysis of HDG Methods for Linearized Shallow Water Equations

Tan Bui-Thanh
SIAM Journal on Scientific Computing 38 (6) A3696 (2016)
https://doi.org/10.1137/16M1057243

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)
https://doi.org/10.1186/s13661-016-0562-2