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## Discontinuous Galerkin and the Crouzeix–Raviart element: Application to elasticity

ESAIM: M2AN, 37 1 (2003) 63-72
Published online: 2003-03-15

## An hp-version error analysis of the discontinuous Galerkin method for linear elasticity

Jianguo Huang and Xuehai Huang
Applied Numerical Mathematics 133 83 (2018)
DOI: 10.1016/j.apnum.2017.12.010

## A locking-free immersed finite element method for planar elasticity interface problems

Tao Lin, Dongwoo Sheen and Xu Zhang
Journal of Computational Physics 247 228 (2013)
DOI: 10.1016/j.jcp.2013.03.053

## Domain Decomposition Methods in Science and Engineering XX

E. Karer, J. K. Kraus and L. T. Zikatanov
Lecture Notes in Computational Science and Engineering, Domain Decomposition Methods in Science and Engineering XX 91 159 (2013)
DOI: 10.1007/978-3-642-35275-1_17

## Encyclopedia of Computational Mechanics Second Edition

F. Auricchio, L. Beirão da Veiga, F. Brezzi and C. Lovadina
Encyclopedia of Computational Mechanics Second Edition 1 (2017)
DOI: 10.1002/9781119176817.ecm2004

## Analysis of DG approximations for Stokes problem based on velocity-pseudostress formulation

Tomás P. Barrios, Rommel Bustinza and Felipe Sánchez
Numerical Methods for Partial Differential Equations 33 (5) 1540 (2017)
DOI: 10.1002/num.22152

## Numerical Approximation of Partial Differential Equations

Sören Bartels
Texts in Applied Mathematics, Numerical Approximation of Partial Differential Equations 64 349 (2016)
DOI: 10.1007/978-3-319-32354-1_8

## Piecewise Divergence-Free Nonconforming Virtual Elements for Stokes Problem in Any Dimensions

Huayi Wei, Xuehai Huang and Ao Li
SIAM Journal on Numerical Analysis 59 (3) 1835 (2021)
DOI: 10.1137/20M1350479

## Numerical Methods and Applications

Francisco J. Gaspar, Carmen Rodrigo, Xiaozhe Hu, et al.
Lecture Notes in Computer Science, Numerical Methods and Applications 11189 3 (2019)
DOI: 10.1007/978-3-030-10692-8_1

## Convergence in the incompressible limit of new discontinuous Galerkin methods with general quadrilateral and hexahedral elements

Beverley J. Grieshaber, Andrew T. McBride and B. Daya Reddy
Computer Methods in Applied Mechanics and Engineering 370 113233 (2020)
DOI: 10.1016/j.cma.2020.113233

## Simulation of rock salt dissolution and its impact on land subsidence

A. Zidane, E. Zechner, P. Huggenberger and A. Younes
Hydrology and Earth System Sciences Discussions 10 (10) 12255 (2013)
DOI: 10.5194/hessd-10-12255-2013

## Connections between discontinuous Galerkin and nonconforming finite element methods for the Stokes equations

Roland Becker, Daniela Capatina and Julie Joie
Numerical Methods for Partial Differential Equations 28 (3) 1013 (2012)
DOI: 10.1002/num.20671

## Analysis and Computation of Microstructure in Finite Plasticity

Carsten Carstensen, Dietmar Gallistl and Boris Krämer
Lecture Notes in Applied and Computational Mechanics, Analysis and Computation of Microstructure in Finite Plasticity 78 1 (2015)
DOI: 10.1007/978-3-319-18242-1_1

## Uniformly Convergent Interior Penalty Methods Using Multilinear Approximations for Problems in Elasticity

B. J. Grieshaber, A. T. McBride and B. D. Reddy
SIAM Journal on Numerical Analysis 53 (5) 2255 (2015)
DOI: 10.1137/140966253

## A Nitsche type method for stress fields calculation in dissimilar material with interface crack

Michael Michaeli, Franck Assous and Anatoly Golubchik
Applied Numerical Mathematics 67 187 (2013)
DOI: 10.1016/j.apnum.2011.08.006

## A Reduced Local Discontinuous Galerkin Method for Nearly Incompressible Linear Elasticity

Xuehai Huang
Mathematical Problems in Engineering 2013 1 (2013)
DOI: 10.1155/2013/546408

## A brick-tetrahedron finite-element interface with stable hybrid explicit–implicit time-stepping for Maxwell’s equations

D. Degerfeldt and T. Rylander
Journal of Computational Physics 220 (1) 383 (2006)
DOI: 10.1016/j.jcp.2006.05.016

## A locking-free discontinuous Galerkin method for linear elasticity in locally nearly incompressible heterogeneous media

Daniele A. Di Pietro and Serge Nicaise
Applied Numerical Mathematics 63 105 (2013)
DOI: 10.1016/j.apnum.2012.09.009

## Meshfree-enriched simplex elements with strain smoothing for the finite element analysis of compressible and nearly incompressible solids

C.T. Wu and W. Hu
Computer Methods in Applied Mechanics and Engineering 200 (45-46) 2991 (2011)
DOI: 10.1016/j.cma.2011.06.013

## The role of the penalty in the local discontinuous Galerkin method for Maxwell’s eigenvalue problem

T. Warburton and Mark Embree
Computer Methods in Applied Mechanics and Engineering 195 (25-28) 3205 (2006)
DOI: 10.1016/j.cma.2005.06.011

## Domain decomposition for linear elasticity with DG jumps and mortars

Vivette Girault, Gergina V. Pencheva, Mary F. Wheeler and Tim M. Wildey
Computer Methods in Applied Mechanics and Engineering 198 (21-26) 1751 (2009)
DOI: 10.1016/j.cma.2008.12.037

## A discontinuous Galerkin formulation for classical and gradient plasticity. Part 2: Algorithms and numerical analysis

J.K. Djoko, F. Ebobisse, A.T. McBride and B.D. Reddy
Computer Methods in Applied Mechanics and Engineering 197 (1-4) 1 (2007)
DOI: 10.1016/j.cma.2007.06.027

## A nonconforming rotated Q1 approximation on tetrahedra

Peter Hansbo
Computer Methods in Applied Mechanics and Engineering 200 (9-12) 1311 (2011)
DOI: 10.1016/j.cma.2010.11.002

## Energy norm a posteriori error estimates for discontinuous Galerkin approximations of the linear elasticity problem

Peter Hansbo and Mats G. Larson
Computer Methods in Applied Mechanics and Engineering 200 (45-46) 3026 (2011)
DOI: 10.1016/j.cma.2011.06.008

## A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations

Blanca Ayuso de Dios, Ivan Georgiev, Johannes Kraus and Ludmil Zikatanov
ESAIM: Mathematical Modelling and Numerical Analysis 47 (5) 1315 (2013)
DOI: 10.1051/m2an/2013070

## Encyclopedia of Computational Mechanics Second Edition

F. Auricchio, L. Beirão da Veiga, F. Brezzi and C. Lovadina
Encyclopedia of Computational Mechanics Second Edition 1 (2017)
DOI: 10.1002/9781119176817.ecm004

## A linear nonconforming finite element method for Maxwell’s equations in two dimensions. Part I: Frequency domain

Peter Hansbo and Thomas Rylander
Journal of Computational Physics 229 (18) 6534 (2010)
DOI: 10.1016/j.jcp.2010.05.009

## The Compact Discontinuous Galerkin Method for Nearly Incompressible Linear Elasticity

Xuehai Huang and Jianguo Huang
Journal of Scientific Computing 56 (2) 291 (2013)
DOI: 10.1007/s10915-012-9676-6

## Adaptive stabilization of discontinuous Galerkin methods for nonlinear elasticity: Motivation, formulation, and numerical examples

Alex Ten Eyck, Fatih Celiker and Adrian Lew
Computer Methods in Applied Mechanics and Engineering 197 (45-48) 3605 (2008)
DOI: 10.1016/j.cma.2008.02.020

## Stabilized Lagrange multiplier methods for bilateral elastic contact with friction

Per Heintz and Peter Hansbo
Computer Methods in Applied Mechanics and Engineering 195 (33-36) 4323 (2006)
DOI: 10.1016/j.cma.2005.09.008

## A posteriori error estimators for stabilized P1 nonconforming approximation of the Stokes problem

Hyung-Chun Lee and Kwang-Yeon Kim
Computer Methods in Applied Mechanics and Engineering 199 (45-48) 2903 (2010)
DOI: 10.1016/j.cma.2010.06.002

## A locking-free and optimally convergent discontinuous-Galerkin-based extended finite element method for cracked nearly incompressible solids

Yongxing Shen and Adrian J. Lew
Computer Methods in Applied Mechanics and Engineering 273 119 (2014)
DOI: 10.1016/j.cma.2014.01.017

## Stabilized discontinuous finite element approximations for Stokes equations

Raytcho Lazarov and Xiu Ye
Journal of Computational and Applied Mathematics 198 (1) 236 (2007)
DOI: 10.1016/j.cam.2005.12.028

## Sea-ice dynamics on triangular grids

Carolin Mehlmann and Peter Korn
Journal of Computational Physics 428 110086 (2021)
DOI: 10.1016/j.jcp.2020.110086

## A domain-specific embedded language in C++ for lowest-order discretizations of diffusive problems on general meshes

Daniele A. Di Pietro, Jean-Marc Gratien and Christophe Prud’homme
BIT Numerical Mathematics 53 (1) 111 (2013)
DOI: 10.1007/s10543-012-0403-3

## Application of a minimal compatible element to incompressible and nearly incompressible continuum mechanics

Erik Burman, Snorre H. Christiansen and Peter Hansbo
Computer Methods in Applied Mechanics and Engineering 369 113224 (2020)
DOI: 10.1016/j.cma.2020.113224

## Guaranteed Lower Bounds for the Elastic Eigenvalues by Using the Nonconforming Crouzeix–Raviart Finite Element

Xuqing Zhang, Yu Zhang and Yidu Yang
Mathematics 8 (8) 1252 (2020)
DOI: 10.3390/math8081252

## An IGA Discontinuous Galerkin Method on the union of overlapped patches

Honghai Zhang, Rong Mo and Neng Wan
Computer Methods in Applied Mechanics and Engineering 326 446 (2017)
DOI: 10.1016/j.cma.2017.08.004

## A geometrically nonlinear FE approach for the simulation of strong and weak discontinuities

Julia Mergheim and Paul Steinmann
Computer Methods in Applied Mechanics and Engineering 195 (37-40) 5037 (2006)
DOI: 10.1016/j.cma.2005.05.057

## A hybrid high-order locking-free method for linear elasticity on general meshes

Daniele A. Di Pietro and Alexandre Ern
Computer Methods in Applied Mechanics and Engineering 283 1 (2015)
DOI: 10.1016/j.cma.2014.09.009

## An extension of the Crouzeix–Raviart space to general meshes with application to quasi-incompressible linear elasticity and Stokes flow

Daniele Di Pietro and Simon Lemaire
Mathematics of Computation 84 (291) 1 (2014)
DOI: 10.1090/S0025-5718-2014-02861-5

## A Consistent Immersed Finite Element Method for the Interface Elasticity Problems

Sangwon Jin, Do Y. Kwak and Daehyeon Kyeong
Advances in Mathematical Physics 2016 1 (2016)
DOI: 10.1155/2016/3292487

## On the Local Discontinuous Galerkin Method for Linear Elasticity

Yuncheng Chen, Jianguo Huang, Xuehai Huang and Yifeng Xu
Mathematical Problems in Engineering 2010 1 (2010)
DOI: 10.1155/2010/759547

## Linear and bilinear immersed finite elements for planar elasticity interface problems

Tao Lin and Xu Zhang
Journal of Computational and Applied Mathematics 236 (18) 4681 (2012)
DOI: 10.1016/j.cam.2012.03.012

## Divergence-Conforming Discontinuous Galerkin Methods and $C^0$ Interior Penalty Methods

Guido Kanschat and Natasha Sharma
SIAM Journal on Numerical Analysis 52 (4) 1822 (2014)
DOI: 10.1137/120902975

## Nonconforming discretizations of convex minimization problems and precise relations to mixed methods

Sören Bartels
Computers & Mathematics with Applications 93 214 (2021)
DOI: 10.1016/j.camwa.2021.04.014

## Primal stabilized hybrid and DG finite element methods for the linear elasticity problem

Cristiane O. Faria, Abimael F.D. Loula and Antônio J.B. dos Santos
Computers & Mathematics with Applications 68 (4) 486 (2014)
DOI: 10.1016/j.camwa.2014.06.014

## Discontinuous Galerkin gradient discretisations for the approximation of second-order differential operators in divergence form

Robert Eymard and Cindy Guichard
Computational and Applied Mathematics 37 (4) 4023 (2018)
DOI: 10.1007/s40314-017-0558-2

## A superconvergent hybridisable discontinuous Galerkin method for linear elasticity

Ruben Sevilla, Matteo Giacomini, Alexandros Karkoulias and Antonio Huerta
International Journal for Numerical Methods in Engineering 116 (2) 91 (2018)
DOI: 10.1002/nme.5916

## Fracture and healing of elastomers: A phase-transition theory and numerical implementation

Aditya Kumar, Gilles A. Francfort and Oscar Lopez-Pamies
Journal of the Mechanics and Physics of Solids 112 523 (2018)
DOI: 10.1016/j.jmps.2018.01.003

## Quasi-Optimal Nonconforming Methods for Symmetric Elliptic Problems. III---Discontinuous Galerkin and Other Interior Penalty Methods

Andreas Veeser and Pietro Zanotti
SIAM Journal on Numerical Analysis 56 (5) 2871 (2018)
DOI: 10.1137/17M1151675

## Convergent numerical method for the Navier–Stokes–Fourier system: a stabilized scheme

IMA Journal of Numerical Analysis 39 (4) 2045 (2019)
DOI: 10.1093/imanum/dry057

## A variational discrete element method for quasistatic and dynamic elastoplasticity

Frédéric Marazzato, Alexandre Ern and Laurent Monasse
International Journal for Numerical Methods in Engineering 121 (23) 5295 (2020)
DOI: 10.1002/nme.6460

## Gradient discretization of two-phase flows coupled with mechanical deformation in fractured porous media

Francesco Bonaldi, Konstantin Brenner, Jérôme Droniou and Roland Masson
Computers & Mathematics with Applications 98 40 (2021)
DOI: 10.1016/j.camwa.2021.06.017

## Encyclopedia of Computational Mechanics

Ferdinando Auricchio, Franco Brezzi and Carlo Lovadina
Encyclopedia of Computational Mechanics (2004)
DOI: 10.1002/0470091355.ecm004

## The nonconforming virtual element method for elasticity problems

Bei Zhang, Jikun Zhao, Yongqin Yang and Shaochun Chen
Journal of Computational Physics 378 394 (2019)
DOI: 10.1016/j.jcp.2018.11.004

## Numerical Mathematics and Advanced Applications ENUMATH 2017

Andreas Veeser and Pietro Zanotti
Lecture Notes in Computational Science and Engineering, Numerical Mathematics and Advanced Applications ENUMATH 2017 126 461 (2019)
DOI: 10.1007/978-3-319-96415-7_41

## A new stabilization technique for the nonconforming Crouzeix–Raviart element applied to linear elasticity

Bishnu P. Lamichhane
Applied Mathematics Letters 39 35 (2015)
DOI: 10.1016/j.aml.2014.08.005

## Stabilized Crouzeix-Raviart element for the Darcy-Stokes problem

Erik Burman and Peter Hansbo
Numerical Methods for Partial Differential Equations 21 (5) 986 (2005)
DOI: 10.1002/num.20076

## A discontinuous finite element method for elasto-plasticity

Peter Hansbo
International Journal for Numerical Methods in Biomedical Engineering n/a (2010)
DOI: 10.1002/cnm.1182

## Stabilized Crouzeix-Raviart element for the coupled Stokes and Darcy problem

Min-fu Feng, Rui-sheng Qi, Rui Zhu and Bing-tao Ju
Applied Mathematics and Mechanics 31 (3) 393 (2010)
DOI: 10.1007/s10483-010-0312-z

## Discontinuous Galerkin methods for non-linear elasticity

A. Ten Eyck and A. Lew
International Journal for Numerical Methods in Engineering 67 (9) 1204 (2006)
DOI: 10.1002/nme.1667

## Numerical Methods and Applications

B. Ayuso, I. Georgiev, J. Kraus and L. Zikatanov
Lecture Notes in Computer Science, Numerical Methods and Applications 6046 353 (2011)
DOI: 10.1007/978-3-642-18466-6_42

## Approximation capabilities of immersed finite element spaces for elasticity Interface problems

Ruchi Guo, Tao Lin and Yanping Lin
Numerical Methods for Partial Differential Equations 35 (3) 1243 (2019)
DOI: 10.1002/num.22348

## Conservative discretizations and parameter‐robust preconditioners for Biot and multiple‐network flux‐based poroelasticity models

Qingguo Hong, Johannes Kraus, Maria Lymbery and Fadi Philo
Numerical Linear Algebra with Applications 26 (4) e2242 (2019)
DOI: 10.1002/nla.2242

## An Immersed Finite Element Method for the Elasticity Problems with Displacement Jump

Daehyeon Kyeong and Do Young Kwak
Advances in Applied Mathematics and Mechanics 9 (2) 407 (2017)
DOI: 10.4208/aamm.2016.m1427

## Discontinuous Galerkin approximations for near-incompressible and near-inextensible transversely isotropic bodies

B.J. Grieshaber, F. Rasolofoson and B.D. Reddy
Computers & Mathematics with Applications 79 (7) 1914 (2020)
DOI: 10.1016/j.camwa.2019.04.016

## A Reduced Crouzeix–Raviart Immersed Finite Element Method for Elasticity Problems with Interfaces

Gwanghyun Jo and Do Young Kwak
Computational Methods in Applied Mathematics (2019)
DOI: 10.1515/cmam-2019-0046

## Simulation of rock salt dissolution and its impact on land subsidence

A. Zidane, E. Zechner, P. Huggenberger and A. Younes
Hydrology and Earth System Sciences 18 (6) 2177 (2014)
DOI: 10.5194/hess-18-2177-2014

## A Multipoint Stress Mixed Finite Element Method for Elasticity on Simplicial Grids

Ilona Ambartsumyan, Eldar Khattatov, Jan M. Nordbotten and Ivan Yotov
SIAM Journal on Numerical Analysis 58 (1) 630 (2020)
DOI: 10.1137/18M1229183

## A low-order nonconforming method for linear elasticity on general meshes

Michele Botti, Daniele A. Di Pietro and Alessandra Guglielmana
Computer Methods in Applied Mechanics and Engineering 354 96 (2019)
DOI: 10.1016/j.cma.2019.05.031

## Error estimates for a partially penalized immersed finite element method for elasticity interface problems

Ruchi Guo, Tao Lin and Yanping Lin
ESAIM: Mathematical Modelling and Numerical Analysis 54 (1) 1 (2020)
DOI: 10.1051/m2an/2019051

## A combination of Crouzeix-Raviart, Discontinuous Galerkin and MPFA methods for buoyancy-driven flows

Anis Younes, Ahmed Makradi, Ali Zidane, Qian Shao and Lyazid Bouhala
International Journal of Numerical Methods for Heat & Fluid Flow 24 (3) 735 (2014)
DOI: 10.1108/HFF-07-2012-0156

## Gradient discretization of two-phase poro-mechanical models with discontinuous pressures at matrix fracture interfaces

Francesco Bonaldi, Konstantin Brenner, Jérôme Droniou, Roland Masson, Antoine Pasteau and Laurent Trenty
ESAIM: Mathematical Modelling and Numerical Analysis 55 (5) 1741 (2021)
DOI: 10.1051/m2an/2021036

## A Robust Finite Element Method for Elastic Vibration Problems

Yuling Guo and Jianguo Huang
Computational Methods in Applied Mathematics (2019)
DOI: 10.1515/cmam-2018-0197

## A locking‐free shifted inverse iteration based on multigrid discretization for the elastic eigenvalue problem

Xuqing Zhang, Yidu Yang and Yu Zhang
Mathematical Methods in the Applied Sciences 44 (7) 5821 (2021)
DOI: 10.1002/mma.7150

## The poker-chip experiments of Gent and Lindley (1959) explained

Journal of the Mechanics and Physics of Solids 150 104359 (2021)
DOI: 10.1016/j.jmps.2021.104359

## Locking-Free and Gradient-Robust $${\varvec{H}}({{\,\mathrm{{\text {div}}}\,}})$$-Conforming HDG Methods for Linear Elasticity

Guosheng Fu, Christoph Lehrenfeld, Alexander Linke and Timo Streckenbach
Journal of Scientific Computing 86 (3) (2021)
DOI: 10.1007/s10915-020-01396-6