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:

This article has been cited by the following article(s):

Error estimation and mesh adaptivity for the virtual element method based on recovery by compatibility in patches

Antonio Maria D'Altri, Stefano Miranda, Luca Patruno, Edoardo Artioli and Carlo Lovadina
International Journal for Numerical Methods in Engineering 121 (19) 4374 (2020)
DOI: 10.1002/nme.6438
See this article

A polygonal discontinuous Galerkin method with minus one stabilization

Silvia Bertoluzza and Daniele Prada
ESAIM: Mathematical Modelling and Numerical Analysis 55 S785 (2021)
DOI: 10.1051/m2an/2020059
See this article

Convergence analysis of virtual element methods for semilinear parabolic problems on polygonal meshes

Dibyendu Adak, E. Natarajan and Sarvesh Kumar
Numerical Methods for Partial Differential Equations 35 (1) 222 (2019)
DOI: 10.1002/num.22298
See this article

Some Estimates for Virtual Element Methods

Susanne C. Brenner, Qingguang Guan and Li-Yeng Sung
Computational Methods in Applied Mathematics 17 (4) (2017)
DOI: 10.1515/cmam-2017-0008
See this article

The NonConforming Virtual Element Method for the Stokes Equations

Andrea Cangiani, Vitaliy Gyrya and Gianmarco Manzini
SIAM Journal on Numerical Analysis 54 (6) 3411 (2016)
DOI: 10.1137/15M1049531
See this article

Preface

L. Beirão da Veiga and A. Ern
ESAIM: Mathematical Modelling and Numerical Analysis 50 (3) 633 (2016)
DOI: 10.1051/m2an/2016034
See this article

A virtual element method for the acoustic vibration problem

Lourenço Beirão da Veiga, David Mora, Gonzalo Rivera and Rodolfo Rodríguez
Numerische Mathematik 136 (3) 725 (2017)
DOI: 10.1007/s00211-016-0855-5
See this article

Conforming and nonconforming virtual element methods for elliptic problems

Andrea Cangiani, Gianmarco Manzini and Oliver J. Sutton
IMA Journal of Numerical Analysis drw036 (2016)
DOI: 10.1093/imanum/drw036
See this article

A Hybrid High-Order Method for Highly Oscillatory Elliptic Problems

Matteo Cicuttin, Alexandre Ern and Simon Lemaire
Computational Methods in Applied Mathematics 19 (4) 723 (2019)
DOI: 10.1515/cmam-2018-0013
See this article

The virtual element method in 50 lines of MATLAB

Oliver J. Sutton
Numerical Algorithms 75 (4) 1141 (2017)
DOI: 10.1007/s11075-016-0235-3
See this article

Parallel solvers for virtual element discretizations of elliptic equations in mixed form

F. Dassi and S. Scacchi
Computers & Mathematics with Applications 79 (7) 1972 (2020)
DOI: 10.1016/j.camwa.2019.07.027
See this article

Multiscale VEM for the Biot consolidation analysis of complex and highly heterogeneous domains

Abhilash Sreekumar, Savvas P. Triantafyllou, François-Xavier Bécot and Fabien Chevillotte
Computer Methods in Applied Mechanics and Engineering 375 113543 (2021)
DOI: 10.1016/j.cma.2020.113543
See this article

Poly-Spline Finite-Element Method

Teseo Schneider, Jérémie Dumas, Xifeng Gao, et al.
ACM Transactions on Graphics 38 (3) 1 (2019)
DOI: 10.1145/3313797
See this article

A nonconforming virtual element method for the Stokes problem on general meshes

Xin Liu, Jian Li and Zhangxin Chen
Computer Methods in Applied Mechanics and Engineering 320 694 (2017)
DOI: 10.1016/j.cma.2017.03.027
See this article

Finite element methods: Research in India over the last decade

Neela Nataraj and A. S. Vasudeva Murthy
Indian Journal of Pure and Applied Mathematics 50 (3) 739 (2019)
DOI: 10.1007/s13226-019-0352-5
See this article

A Hybrid High-Order Discretization Combined with Nitsche's Method for Contact and Tresca Friction in Small Strain Elasticity

Franz Chouly, Alexandre Ern and Nicolas Pignet
SIAM Journal on Scientific Computing 42 (4) A2300 (2020)
DOI: 10.1137/19M1286499
See this article

On the virtual element method for topology optimization on polygonal meshes: A numerical study

P.F. Antonietti, M. Bruggi, S. Scacchi and M. Verani
Computers & Mathematics with Applications 74 (5) 1091 (2017)
DOI: 10.1016/j.camwa.2017.05.025
See this article

A multigrid algorithm for the p-version of the virtual element method

Paola F. Antonietti, Lorenzo Mascotto and Marco Verani
ESAIM: Mathematical Modelling and Numerical Analysis 52 (1) 337 (2018)
DOI: 10.1051/m2an/2018007
See this article

Virtual element method for semilinear hyperbolic problems on polygonal meshes

Dibyendu Adak, E. Natarajan and Sarvesh Kumar
International Journal of Computer Mathematics 96 (5) 971 (2019)
DOI: 10.1080/00207160.2018.1475651
See this article

Anisotropic Error Estimates of the Linear Virtual Element Method on Polygonal Meshes

Shuhao Cao and Long Chen
SIAM Journal on Numerical Analysis 56 (5) 2913 (2018)
DOI: 10.1137/17M1154369
See this article

The nonconforming virtual element method for plate bending problems

Jikun Zhao, Shaochun Chen and Bei Zhang
Mathematical Models and Methods in Applied Sciences 26 (09) 1671 (2016)
DOI: 10.1142/S021820251650041X
See this article

Ws,p-approximation properties of elliptic projectors on polynomial spaces, with application to the error analysis of a Hybrid High-Order discretisation of Leray–Lions problems

Daniele A. Di Pietro and Jérôme Droniou
Mathematical Models and Methods in Applied Sciences 27 (05) 879 (2017)
DOI: 10.1142/S0218202517500191
See this article

The nonconforming virtual element method for the Darcy–Stokes problem

Jikun Zhao, Bei Zhang, Shipeng Mao and Shaochun Chen
Computer Methods in Applied Mechanics and Engineering 370 113251 (2020)
DOI: 10.1016/j.cma.2020.113251
See this article

Virtual Elements for the Navier--Stokes Problem on Polygonal Meshes

L. Beira͂o da Veiga, C. Lovadina and G. Vacca
SIAM Journal on Numerical Analysis 56 (3) 1210 (2018)
DOI: 10.1137/17M1132811
See this article

The fully nonconforming virtual element method for biharmonic problems

P. F. Antonietti, G. Manzini and M. Verani
Mathematical Models and Methods in Applied Sciences 28 (02) 387 (2018)
DOI: 10.1142/S0218202518500100
See this article

An Unfitted Hybrid High-Order Method for Elliptic Interface Problems

Erik Burman and Alexandre Ern
SIAM Journal on Numerical Analysis 56 (3) 1525 (2018)
DOI: 10.1137/17M1154266
See this article

Virtual element method for semilinear sine–Gordon equation over polygonal mesh using product approximation technique

D. Adak and S. Natarajan
Mathematics and Computers in Simulation 172 224 (2020)
DOI: 10.1016/j.matcom.2019.12.007
See this article

Virtual element method for second-order elliptic eigenvalue problems

Francesca Gardini and Giuseppe Vacca
IMA Journal of Numerical Analysis 38 (4) 2026 (2018)
DOI: 10.1093/imanum/drx063
See this article

The arbitrary‐order virtual element method for linear elastodynamics models: convergence, stability and dispersion‐dissipation analysis

Paola F. Antonietti, Gianmarco Manzini, Ilario Mazzieri, Hashem M. Mourad and Marco Verani
International Journal for Numerical Methods in Engineering 122 (4) 934 (2021)
DOI: 10.1002/nme.6569
See this article

High-order Virtual Element Method on polyhedral meshes

L. Beirão da Veiga, F. Dassi and A. Russo
Computers & Mathematics with Applications 74 (5) 1110 (2017)
DOI: 10.1016/j.camwa.2017.03.021
See this article

Fast Numerical Integration on Polytopic Meshes with Applications to Discontinuous Galerkin Finite Element Methods

Paola F. Antonietti, Paul Houston and Giorgio Pennesi
Journal of Scientific Computing 77 (3) 1339 (2018)
DOI: 10.1007/s10915-018-0802-y
See this article

A nonconforming Trefftz virtual element method for the Helmholtz problem

Lorenzo Mascotto, Ilaria Perugia and Alexander Pichler
Mathematical Models and Methods in Applied Sciences 29 (09) 1619 (2019)
DOI: 10.1142/S0218202519500301
See this article

A posteriori error estimates for the virtual element method

Andrea Cangiani, Emmanuil H. Georgoulis, Tristan Pryer and Oliver J. Sutton
Numerische Mathematik 137 (4) 857 (2017)
DOI: 10.1007/s00211-017-0891-9
See this article

A plane wave virtual element method for the Helmholtz problem

Ilaria Perugia, Paola Pietra and Alessandro Russo
ESAIM: Mathematical Modelling and Numerical Analysis 50 (3) 783 (2016)
DOI: 10.1051/m2an/2015066
See this article

A fully discrete virtual element scheme for the Cahn–Hilliard equation in mixed form

Xin Liu, Zhengkang He and Zhangxin Chen
Computer Physics Communications 246 106870 (2020)
DOI: 10.1016/j.cpc.2019.106870
See this article

A virtual element method for the Cahn–Hilliard problem in mixed form

Xin Liu and Zhangxin Chen
Applied Mathematics Letters 87 115 (2019)
DOI: 10.1016/j.aml.2018.07.031
See this article

A Hybrid High‐Order method for finite elastoplastic deformations within a logarithmic strain framework

Mickaël Abbas, Alexandre Ern and Nicolas Pignet
International Journal for Numerical Methods in Engineering 120 (3) 303 (2019)
DOI: 10.1002/nme.6137
See this article

SUPG stabilization for the nonconforming virtual element method for advection–diffusion–reaction equations

S. Berrone, A. Borio and G. Manzini
Computer Methods in Applied Mechanics and Engineering 340 500 (2018)
DOI: 10.1016/j.cma.2018.05.027
See this article

Virtual element methods for nonlocal parabolic problems on general type of meshes

D. Adak and S. Natarajan
Advances in Computational Mathematics 46 (5) (2020)
DOI: 10.1007/s10444-020-09811-0
See this article

Virtual Element Method for the Laplace-Beltrami equation on surfaces

Massimo Frittelli and Ivonne Sgura
ESAIM: Mathematical Modelling and Numerical Analysis 52 (3) 965 (2018)
DOI: 10.1051/m2an/2017040
See this article

Virtual element method for quasilinear elliptic problems

A Cangiani, P Chatzipantelidis, G Diwan and E H Georgoulis
IMA Journal of Numerical Analysis 40 (4) 2450 (2020)
DOI: 10.1093/imanum/drz035
See this article

A quasi-optimal variant of the hybrid high-order method for elliptic partial differential equations with H−1 loads

Alexandre Ern and Pietro Zanotti
IMA Journal of Numerical Analysis 40 (4) 2163 (2020)
DOI: 10.1093/imanum/drz057
See this article

A New Projection-Based Stabilized Virtual Element Method for the Stokes Problem

Jun Guo and Minfu Feng
Journal of Scientific Computing 85 (1) (2020)
DOI: 10.1007/s10915-020-01301-1
See this article

n-sided polygonal hybrid finite elements with unified fundamental solution kernels for topology optimization

Hui Wang, Qing-Hua Qin and Cheuk-Yu Lee
Applied Mathematical Modelling 66 97 (2019)
DOI: 10.1016/j.apm.2018.09.014
See this article

Nonconforming Virtual Element Method for the Time Fractional Reaction–Subdiffusion Equation with Non-smooth Data

Meng Li, Jikun Zhao, Chengming Huang and Shaochun Chen
Journal of Scientific Computing 81 (3) 1823 (2019)
DOI: 10.1007/s10915-019-01064-4
See this article

A virtual element method for the coupled Stokes–Darcy problem with the Beaver–Joseph–Saffman interface condition

Xin Liu, Rui Li and Zhangxin Chen
Calcolo 56 (4) (2019)
DOI: 10.1007/s10092-019-0345-0
See this article

Non-conforming Harmonic Virtual Element Method: $$h$$h- and $$p$$p-Versions

Lorenzo Mascotto, Ilaria Perugia and Alexander Pichler
Journal of Scientific Computing 77 (3) 1874 (2018)
DOI: 10.1007/s10915-018-0797-4
See this article

A Hybrid High-Order method for the incompressible Navier–Stokes equations based on Temam's device

Lorenzo Botti, Daniele A. Di Pietro and Jérôme Droniou
Journal of Computational Physics 376 786 (2019)
DOI: 10.1016/j.jcp.2018.10.014
See this article

A high-order conservative remap for discontinuous Galerkin schemes on curvilinear polygonal meshes

Konstantin Lipnikov and Nathaniel Morgan
Journal of Computational Physics 399 108931 (2019)
DOI: 10.1016/j.jcp.2019.108931
See this article

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
See this article

A nonconforming Trefftz virtual element method for the Helmholtz problem: Numerical aspects

Lorenzo Mascotto, Ilaria Perugia and Alexander Pichler
Computer Methods in Applied Mechanics and Engineering 347 445 (2019)
DOI: 10.1016/j.cma.2018.12.039
See this article

A posteriori error estimates for a Virtual Element Method for the Steklov eigenvalue problem

David Mora, Gonzalo Rivera and Rodolfo Rodríguez
Computers & Mathematics with Applications 74 (9) 2172 (2017)
DOI: 10.1016/j.camwa.2017.05.016
See this article

Serendipity Virtual Elements for General Elliptic Equations in Three Dimensions

Lourenço Beirão Da Veiga, Franco Brezzi, Franco Dassi, Luisa Donatelia Marini and Alessandro Russo
Chinese Annals of Mathematics, Series B 39 (2) 315 (2018)
DOI: 10.1007/s11401-018-1066-4
See this article

Nonconforming virtual element method for 2mth order partial differential equations in $${\mathbb {R}}^n$$ with $$m>n$$

Xuehai Huang
Calcolo 57 (4) (2020)
DOI: 10.1007/s10092-020-00381-7
See this article

The nonconforming virtual element method for the Navier-Stokes equations

Xin Liu and Zhangxin Chen
Advances in Computational Mathematics 45 (1) 51 (2019)
DOI: 10.1007/s10444-018-9602-z
See this article

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)
DOI: 10.1515/cmam-2017-0009
See this article

An Advection-Robust Hybrid High-Order Method for the Oseen Problem

Joubine Aghili and Daniele A. Di Pietro
Journal of Scientific Computing 77 (3) 1310 (2018)
DOI: 10.1007/s10915-018-0681-2
See this article

The conforming virtual element method for polyharmonic problems

P.F. Antonietti, G. Manzini and M. Verani
Computers & Mathematics with Applications 79 (7) 2021 (2020)
DOI: 10.1016/j.camwa.2019.09.022
See this article

The nonconforming virtual element method for parabolic problems

Jikun Zhao, Bei Zhang and Xiaopeng Zhu
Applied Numerical Mathematics 143 97 (2019)
DOI: 10.1016/j.apnum.2019.04.002
See this article

Extension of the nonconforming Trefftz virtual element method to the Helmholtz problem with piecewise constant wave number

Lorenzo Mascotto and Alexander Pichler
Applied Numerical Mathematics 155 160 (2020)
DOI: 10.1016/j.apnum.2019.04.005
See this article

A medius error analysis for nonconforming virtual element methods for Poisson and biharmonic equations

Jianguo Huang and Yue Yu
Journal of Computational and Applied Mathematics 386 113229 (2021)
DOI: 10.1016/j.cam.2020.113229
See this article

Anisotropic Error Estimates of the Linear Nonconforming Virtual Element Methods

Shuhao Cao and Long Chen
SIAM Journal on Numerical Analysis 57 (3) 1058 (2019)
DOI: 10.1137/18M1196455
See this article

An extended P1-nonconforming finite element method on general polytopal partitions

Yujie Liu and Junping Wang
Journal of Computational and Applied Mathematics 381 113021 (2021)
DOI: 10.1016/j.cam.2020.113021
See this article

Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming

M. Cicuttin, D.A. Di Pietro and A. Ern
Journal of Computational and Applied Mathematics 344 852 (2018)
DOI: 10.1016/j.cam.2017.09.017
See this article

A divergence-free reconstruction of the nonconforming virtual element method for the Stokes problem

Xin Liu, Rui Li and Yufeng Nie
Computer Methods in Applied Mechanics and Engineering 372 113351 (2020)
DOI: 10.1016/j.cma.2020.113351
See this article

The Divergence-Free Nonconforming Virtual Element for the Stokes Problem

Jikun Zhao, Bei Zhang, Shipeng Mao and Shaochun Chen
SIAM Journal on Numerical Analysis 57 (6) 2730 (2019)
DOI: 10.1137/18M1200762
See this article

The Nonconforming Virtual Element Method for a Stationary Stokes Hemivariational Inequality with Slip Boundary Condition

Min Ling, Fei Wang and Weimin Han
Journal of Scientific Computing 85 (3) (2020)
DOI: 10.1007/s10915-020-01333-7
See this article

A multiscale virtual element method for the analysis of heterogeneous media

Abhilash Sreekumar, Savvas P. Triantafyllou, François‐Xavier Bécot and Fabien Chevillotte
International Journal for Numerical Methods in Engineering 121 (8) 1791 (2020)
DOI: 10.1002/nme.6287
See this article

Bridging the hybrid high-order and virtual element methods

Simon Lemaire
IMA Journal of Numerical Analysis 41 (1) 549 (2021)
DOI: 10.1093/imanum/drz056
See this article

Hybrid high-order discretizations combined with Nitsche’s method for Dirichlet and Signorini boundary conditions

Karol L Cascavita, Franz Chouly and Alexandre Ern
IMA Journal of Numerical Analysis 40 (4) 2189 (2020)
DOI: 10.1093/imanum/drz038
See this article

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)
DOI: 10.1016/j.camwa.2019.10.018
See this article

The nonconforming virtual element method for fourth-order singular perturbation problem

Bei Zhang, Jikun Zhao and Shaochun Chen
Advances in Computational Mathematics 46 (2) (2020)
DOI: 10.1007/s10444-020-09743-9
See this article

A Hybrid High-Order method for incremental associative plasticity with small deformations

Mickaël Abbas, Alexandre Ern and Nicolas Pignet
Computer Methods in Applied Mechanics and Engineering 346 891 (2019)
DOI: 10.1016/j.cma.2018.08.037
See this article

A hybrid high‐order formulation for a Neumann problem on polytopal meshes

Rommel Bustinza and Jonathan Munguia‐La‐Cotera
Numerical Methods for Partial Differential Equations 36 (3) 524 (2020)
DOI: 10.1002/num.22439
See this article

The nonconforming Virtual Element Method for eigenvalue problems

Francesca Gardini, Gianmarco Manzini and Giuseppe Vacca
ESAIM: Mathematical Modelling and Numerical Analysis 53 (3) 749 (2019)
DOI: 10.1051/m2an/2018074
See this article

Unified formulation and analysis of mixed and primal discontinuous skeletal methods on polytopal meshes

Daniele Boffi and Daniele A. Di Pietro
ESAIM: Mathematical Modelling and Numerical Analysis 52 (1) 1 (2018)
DOI: 10.1051/m2an/2017036
See this article

Hybrid High-Order Methods for the Elliptic Obstacle Problem

Matteo Cicuttin, Alexandre Ern and Thirupathi Gudi
Journal of Scientific Computing 83 (1) (2020)
DOI: 10.1007/s10915-020-01195-z
See this article

The Hybrid High-Order Method for Polytopal Meshes

Daniele Antonio Di Pietro and Jérôme Droniou
MS&A, The Hybrid High-Order Method for Polytopal Meshes 19 185 (2020)
DOI: 10.1007/978-3-030-37203-3_5
See this article

Some error analysis on virtual element methods

Long Chen and Jianguo Huang
Calcolo 55 (1) (2018)
DOI: 10.1007/s10092-018-0249-4
See this article

Discontinuous Skeletal Gradient Discretisation methods on polytopal meshes

Daniele A. Di Pietro, Jérôme Droniou and Gianmarco Manzini
Journal of Computational Physics 355 397 (2018)
DOI: 10.1016/j.jcp.2017.11.018
See this article

Polynomial preserving virtual elements with curved edges

L. Beirão da Veiga, F. Brezzi, L. D. Marini and A. Russo
Mathematical Models and Methods in Applied Sciences 30 (08) 1555 (2020)
DOI: 10.1142/S0218202520500311
See this article

A posteriori error estimation and adaptivity in hp virtual elements

L. Beirão da Veiga, G. Manzini and L. Mascotto
Numerische Mathematik 143 (1) 139 (2019)
DOI: 10.1007/s00211-019-01054-6
See this article

Virtual element methods for the spatial discretisation of the multigroup neutron diffusion equation on polygonal meshes with applications to nuclear reactor physics

J.A. Ferguson, J. Kópházi and M.D. Eaton
Annals of Nuclear Energy 151 107884 (2021)
DOI: 10.1016/j.anucene.2020.107884
See this article

Finite Elements and Virtual Elements on Classical Meshes

Franco Brezzi and Luisa Donatella Marini
Vietnam Journal of Mathematics (2021)
DOI: 10.1007/s10013-021-00474-y
See this article

Design and convergence analysis of numerical methods for stochastic evolution equations with Leray–Lions operator

Jérôme Droniou, Beniamin Goldys and Kim-Ngan Le
IMA Journal of Numerical Analysis (2021)
DOI: 10.1093/imanum/draa105
See this article

Robust nonconforming virtual element methods for general fourth-order problems with varying coefficients

Andreas Dedner and Alice Hodson
IMA Journal of Numerical Analysis (2021)
DOI: 10.1093/imanum/drab003
See this article

Conforming and nonconforming conservative virtual element methods for nonlinear Schrödinger equation: A unified framework

Meng Li, Jikun Zhao, Nan Wang and Shaochun Chen
Computer Methods in Applied Mechanics and Engineering 380 113793 (2021)
DOI: 10.1016/j.cma.2021.113793
See this article

Conservative high-order discontinuous Galerkin remap scheme on curvilinear polyhedral meshes

Konstantin Lipnikov and Nathaniel Morgan
Journal of Computational Physics 420 109712 (2020)
DOI: 10.1016/j.jcp.2020.109712
See this article