EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues ESAIM: M2AN, 49 2 (2015) 577-599 Article references

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:

Numerical solution of nonlinear convection-diffusion-reaction equation using a stabilized virtual element method

M. Arrutselvi, E. Natarajan and S. Natarajan
Computers & Mathematics with Applications 183 46 (2025)
https://doi.org/10.1016/j.camwa.2025.01.034

Goal-oriented dual-weighted residual error estimation for the Virtual Elements Method

C. Sellmann and P. Junker
Computer Methods in Applied Mechanics and Engineering 443 118034 (2025)
https://doi.org/10.1016/j.cma.2025.118034

Generalised gradients for virtual elements and applications to a posteriori error analysis

Théophile Chaumont-Frelet, Joscha Gedicke and Lorenzo Mascotto
Mathematics of Computation (2025)
https://doi.org/10.1090/mcom/4092

Nonconforming virtual element method for the Schrödinger eigenvalue problem

Dibyendu Adak, Gianmarco Manzini and Jesus Vellojin
Computers & Mathematics with Applications 182 213 (2025)
https://doi.org/10.1016/j.camwa.2025.01.035

On mesh refinement procedures for polygonal virtual elements

Daniel van Huyssteen, Felipe Lopez Rivarola, Guillermo Etse and Paul Steinmann
Applications in Engineering Science 22 100222 (2025)
https://doi.org/10.1016/j.apples.2025.100222

Lowest order stabilization free virtual element method for the 2D Poisson equation

Stefano Berrone, Andrea Borio and Francesca Marcon
Computers & Mathematics with Applications 177 78 (2025)
https://doi.org/10.1016/j.camwa.2024.11.017

Quasi-optimal mesh generation for the virtual element method: A fully adaptive remeshing procedure

Daniel van Huyssteen, Felipe Lopez Rivarola, Guillermo Etse and Paul Steinmann
Computer Methods in Applied Mechanics and Engineering 435 117630 (2025)
https://doi.org/10.1016/j.cma.2024.117630

VEM approximation for the Stokes eigenvalue problem: A priori and a posteriori error analysis

Dibyendu Adak, Felipe Lepe and Gonzalo Rivera
Computer Methods in Applied Mechanics and Engineering 444 118156 (2025)
https://doi.org/10.1016/j.cma.2025.118156

A $$C^1$$-Conforming Arbitrary-Order Two-Dimensional Virtual Element Method for the Fourth-Order Phase-Field Equation

Dibyendu Adak, Gianmarco Manzini, Hashem M. Mourad, JeeYeon N. Plohr and Lampros Svolos
Journal of Scientific Computing 98 (2) (2024)
https://doi.org/10.1007/s10915-023-02409-w

Adaptive VEM for variable data: convergence and optimality

L Beirão da Veiga, C Canuto, R H Nochetto, G Vacca and M Verani
IMA Journal of Numerical Analysis 44 (5) 2553 (2024)
https://doi.org/10.1093/imanum/drad085

On adaptive mesh coarsening procedures for the virtual element method for two-dimensional elastic problems

Daniel van Huyssteen, Felipe Lopez Rivarola, Guillermo Etse and Paul Steinmann
Computer Methods in Applied Mechanics and Engineering 418 116507 (2024)
https://doi.org/10.1016/j.cma.2023.116507

Residual-based a posteriori error estimation for mixed virtual element methods

Mauricio Munar, Andrea Cangiani and Iván Velásquez
Computers & Mathematics with Applications 166 182 (2024)
https://doi.org/10.1016/j.camwa.2024.05.011

A posteriori error analysis and mesh adaptivity for a virtual element method solving the Stokes equations

Gianmarco Manzini and Annamaria Mazzia
Mathematics and Computers in Simulation 221 19 (2024)
https://doi.org/10.1016/j.matcom.2024.01.022

A lowest-order locking-free nonconforming virtual element method based on the reduced integration technique for linear elasticity problems

Yue Yu
Computers & Mathematics with Applications 135 157 (2023)
https://doi.org/10.1016/j.camwa.2023.01.030

A Posteriori Error Analysis of the Hybrid High-Order Method for the Stokes Problem

Yongchao Zhang, Liquan Mei and Gang Wang
Journal of Scientific Computing 96 (3) (2023)
https://doi.org/10.1007/s10915-023-02291-6

Gradient recovery type a posteriori error estimates of virtual element method for an elliptic variational inequality of the second kind

Huayi Wei, Yanling Deng and Fei Wang
Nonlinear Analysis: Real World Applications 73 103903 (2023)
https://doi.org/10.1016/j.nonrwa.2023.103903

An Introductory Review on A Posteriori Error Estimation in Finite Element Computations

Ludovic Chamoin and Frédéric Legoll
SIAM Review 65 (4) 963 (2023)
https://doi.org/10.1137/21M1464841

A fully-discrete virtual element method for the nonstationary Boussinesq equations in stream-function form

L. Beirão da Veiga, D. Mora and A. Silgado
Computer Methods in Applied Mechanics and Engineering 408 115947 (2023)
https://doi.org/10.1016/j.cma.2023.115947

A posteriori error analysis and adaptivity for a VEM discretization of the Navier–Stokes equations

Claudio Canuto and Davide Rosso
Advances in Computational Mathematics 49 (6) (2023)
https://doi.org/10.1007/s10444-023-10081-9

Adaptive VEM: Stabilization-Free A Posteriori Error Analysis and Contraction Property

L. Beirão da Veiga, C. Canuto, R. H. Nochetto, G. Vacca and M. Verani
SIAM Journal on Numerical Analysis 61 (2) 457 (2023)
https://doi.org/10.1137/21M1458740

A first-order stabilization-free Virtual Element Method

Stefano Berrone, Andrea Borio, Francesca Marcon and Gioana Teora
Applied Mathematics Letters 142 108641 (2023)
https://doi.org/10.1016/j.aml.2023.108641

A posteriori virtual element method for the acoustic vibration problem

F. Lepe, D. Mora, G. Rivera and I. Velásquez
Advances in Computational Mathematics 49 (1) (2023)
https://doi.org/10.1007/s10444-022-10003-1

Higher-order adaptive virtual element methods with contraction properties

Claudio Canuto and Davide Fassino
Mathematics in Engineering 5 (6) 1 (2023)
https://doi.org/10.3934/mine.2023101

A priori and a posteriori error analysis for virtual element discretization of elliptic optimal control problem

Qiming Wang and Zhaojie Zhou
Numerical Algorithms 90 (3) 989 (2022)
https://doi.org/10.1007/s11075-021-01219-1

The Virtual Element Method and its Applications

Sebastian Naranjo Alvarez, Vrushali A. Bokil, Vitaliy Gyrya and Gianmarco Manzini
SEMA SIMAI Springer Series, The Virtual Element Method and its Applications 31 499 (2022)
https://doi.org/10.1007/978-3-030-95319-5_12

The Virtual Element Method and its Applications

Dibyendu Adak, M. Arrutselvi, E. Natarajan and S. Natarajan
SEMA SIMAI Springer Series, The Virtual Element Method and its Applications 31 59 (2022)
https://doi.org/10.1007/978-3-030-95319-5_2

The role of mesh quality and mesh quality indicators in the virtual element method

T. Sorgente, S. Biasotti, G. Manzini and M. Spagnuolo
Advances in Computational Mathematics 48 (1) (2022)
https://doi.org/10.1007/s10444-021-09913-3

Anisotropic a posteriori error estimate for the virtual element method

P F Antonietti, S Berrone, A Borio, et al.
IMA Journal of Numerical Analysis 42 (2) 1273 (2022)
https://doi.org/10.1093/imanum/drab001

Virtual element approximation of two-dimensional parabolic variational inequalities

D. Adak, G. Manzini and S. Natarajan
Computers & Mathematics with Applications 116 48 (2022)
https://doi.org/10.1016/j.camwa.2021.09.007

A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem

Gianmarco Manzini and Annamaria Mazzia
Journal of Computational Dynamics 9 (2) 207 (2022)
https://doi.org/10.3934/jcd.2021020

Polyhedral mesh quality indicator for the Virtual Element Method

T. Sorgente, S. Biasotti, G. Manzini and M. Spagnuolo
Computers & Mathematics with Applications 114 151 (2022)
https://doi.org/10.1016/j.camwa.2022.03.042

A new quality preserving polygonal mesh refinement algorithm for Polygonal Element Methods

Stefano Berrone and Alessandro D’Auria
Finite Elements in Analysis and Design 207 103770 (2022)
https://doi.org/10.1016/j.finel.2022.103770

$ C^1 $-VEM for some variants of the Cahn-Hilliard equation: A numerical exploration

Paola F. Antonietti, Simone Scacchi, Giuseppe Vacca and Marco Verani
Discrete and Continuous Dynamical Systems - S 15 (8) 1919 (2022)
https://doi.org/10.3934/dcdss.2022038

A priori and a posteriori error analysis of the lowest-order NCVEM for second-order linear indefinite elliptic problems

Carsten Carstensen, Rekha Khot and Amiya K. Pani
Numerische Mathematik 151 (3) 551 (2022)
https://doi.org/10.1007/s00211-022-01296-x

A posteriori error estimation for a C1 virtual element method of Kirchhoff plates

Mingqing Chen, Jianguo Huang and Sen Lin
Computers & Mathematics with Applications 120 132 (2022)
https://doi.org/10.1016/j.camwa.2022.05.001

The Virtual Element Method and its Applications

Edoardo Artioli, Stefano de Miranda, Carlo Lovadina, Luca Patruno and Michele Visinoni
SEMA SIMAI Springer Series, The Virtual Element Method and its Applications 31 137 (2022)
https://doi.org/10.1007/978-3-030-95319-5_4

The Virtual Element Method and its Applications

Tommaso Sorgente, Daniele Prada, Daniela Cabiddu, et al.
SEMA SIMAI Springer Series, The Virtual Element Method and its Applications 31 1 (2022)
https://doi.org/10.1007/978-3-030-95319-5_1

The Virtual Element Method and its Applications

Paola F. Antonietti, Gianmarco Manzini, Ilario Mazzieri, Simone Scacchi and Marco Verani
SEMA SIMAI Springer Series, The Virtual Element Method and its Applications 31 411 (2022)
https://doi.org/10.1007/978-3-030-95319-5_10

On mesh refinement procedures for the virtual element method for two-dimensional elastic problems

Daniel van Huyssteen, Felipe Lopez Rivarola, Guillermo Etse and Paul Steinmann
Computer Methods in Applied Mechanics and Engineering 393 114849 (2022)
https://doi.org/10.1016/j.cma.2022.114849

Virtual element method for the Helmholtz transmission eigenvalue problem of anisotropic media

Jian Meng and Liquan Mei
Mathematical Models and Methods in Applied Sciences 32 (08) 1493 (2022)
https://doi.org/10.1142/S0218202522500348

A posteriori error analysis of a non-consistent virtual element method for reaction diffusion equations

Jianguo Huang and Sen Lin
Applied Mathematics Letters 122 107531 (2021)
https://doi.org/10.1016/j.aml.2021.107531

Polyhedral Methods in Geosciences

Dibyendu Adak, Gianmarco Manzini and Sundararajan Natarajan
SEMA SIMAI Springer Series, Polyhedral Methods in Geosciences 27 259 (2021)
https://doi.org/10.1007/978-3-030-69363-3_7

Least‐squares virtual element method for the convection‐diffusion‐reaction problem

Gang Wang, Ying Wang and Yinnian He
International Journal for Numerical Methods in Engineering 122 (11) 2672 (2021)
https://doi.org/10.1002/nme.6636

Error estimation for the polygonal finite element method for smooth and singular linear elasticity

Octavio A. González-Estrada, Sundararajan Natarajan, Juan José Ródenas and Stéphane P.A. Bordas
Computers & Mathematics with Applications 92 109 (2021)
https://doi.org/10.1016/j.camwa.2021.03.017

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)
https://doi.org/10.1016/j.cam.2020.113229

Virtual element method for nonlinear convection–diffusion–reaction equation on polygonal meshes

M. Arrutselvi and E. Natarajan
International Journal of Computer Mathematics 98 (9) 1852 (2021)
https://doi.org/10.1080/00207160.2020.1849637

Adaptive Virtual Element Method for Optimal Control Problem Governed by General Elliptic Equation

Qiming Wang and Zhaojie Zhou
Journal of Scientific Computing 88 (1) (2021)
https://doi.org/10.1007/s10915-021-01528-6

A review on arbitrarily regular conforming virtual element methods for second- and higher-order elliptic partial differential equations

Paola F. Antonietti, Gianmarco Manzini, Simone Scacchi and Marco Verani
Mathematical Models and Methods in Applied Sciences 31 (14) 2825 (2021)
https://doi.org/10.1142/S0218202521500627

Adaptive non-hierarchical Galerkin methods for parabolic problems with application to moving mesh and virtual element methods

Andrea Cangiani, Emmanuil H. Georgoulis and Oliver J. Sutton
Mathematical Models and Methods in Applied Sciences 31 (04) 711 (2021)
https://doi.org/10.1142/S0218202521500172

A posteriori error estimate for discontinuous Galerkin finite element method on polytopal mesh

Jintao Cui, Fuzheng Gao, Zhengjia Sun and Peng Zhu
Numerical Methods for Partial Differential Equations 36 (3) 601 (2020)
https://doi.org/10.1002/num.22443

An adaptive curved virtual element method for the statistical homogenization of random fibre-reinforced composites

E. Artioli, L. Beirão da Veiga and M. Verani
Finite Elements in Analysis and Design 177 103418 (2020)
https://doi.org/10.1016/j.finel.2020.103418

A posteriori error analysis of a mixed virtual element method for a nonlinear Brinkman model of porous media flow

Mauricio Munar and Filánder A. Sequeira
Computers & Mathematics with Applications 80 (5) 1240 (2020)
https://doi.org/10.1016/j.camwa.2020.06.005

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

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

A priori and a posteriori error estimates for a virtual element spectral analysis for the elasticity equations

David Mora and Gonzalo Rivera
IMA Journal of Numerical Analysis 40 (1) 322 (2020)
https://doi.org/10.1093/imanum/dry063

A virtual element method for a nonlocal FitzHugh–Nagumo model of cardiac electrophysiology

Mauricio Sepúlveda, David Mora, Mostafa Bendahmane and Verónica Anaya
IMA Journal of Numerical Analysis 40 (2) 1544 (2020)
https://doi.org/10.1093/imanum/drz001

Virtual element method for a nonlocal elliptic problem of Kirchhoff type on polygonal meshes

D. Adak and S. Natarajan
Computers & Mathematics with Applications 79 (10) 2856 (2020)
https://doi.org/10.1016/j.camwa.2019.12.018

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)
https://doi.org/10.1051/m2an/2018074

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)
https://doi.org/10.1080/00207160.2018.1475651

A simple and effective gradient recovery scheme and a posteriori error estimator for the Virtual Element Method (VEM)

Heng Chi, Lourenço Beirão da Veiga and Glaucio H. Paulino
Computer Methods in Applied Mechanics and Engineering 347 21 (2019)
https://doi.org/10.1016/j.cma.2018.08.014

Anisotropic polygonal and polyhedral discretizations in finite element analysis

Steffen Weißer
ESAIM: Mathematical Modelling and Numerical Analysis 53 (2) 475 (2019)
https://doi.org/10.1051/m2an/2018066

Superconvergent gradient recovery for virtual element methods

Hailong Guo, Cong Xie and Ren Zhao
Mathematical Models and Methods in Applied Sciences 29 (11) 2007 (2019)
https://doi.org/10.1142/S0218202519500386

Numerical Mathematics and Advanced Applications ENUMATH 2017

Paola F. Antonietti, Stefano Berrone, Marco Verani and Steffen Weißer
Lecture Notes in Computational Science and Engineering, Numerical Mathematics and Advanced Applications ENUMATH 2017 126 725 (2019)
https://doi.org/10.1007/978-3-319-96415-7_67

The Dual-Weighted Residual Estimator Realized on Polygonal Meshes

Steffen Weißer and Thomas Wick
Computational Methods in Applied Mathematics 18 (4) 753 (2018)
https://doi.org/10.1515/cmam-2017-0046

Virtual element method for second-order elliptic eigenvalue problems

Francesca Gardini and Giuseppe Vacca
IMA Journal of Numerical Analysis 38 (4) 2026 (2018)
https://doi.org/10.1093/imanum/drx063

A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows

Martin Vohralík and Soleiman Yousef
Computer Methods in Applied Mechanics and Engineering 331 728 (2018)
https://doi.org/10.1016/j.cma.2017.11.027

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)
https://doi.org/10.1016/j.cma.2018.05.027

A residual a posteriori error estimate for the Virtual Element Method

Stefano Berrone and Andrea Borio
Mathematical Models and Methods in Applied Sciences 27 (08) 1423 (2017)
https://doi.org/10.1142/S0218202517500233

Residual based error estimate and quasi-interpolation on polygonal meshes for high order BEM-based FEM

Steffen Weißer
Computers & Mathematics with Applications 73 (2) 187 (2017)
https://doi.org/10.1016/j.camwa.2016.11.013

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)
https://doi.org/10.1007/s00211-017-0891-9

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)
https://doi.org/10.1016/j.camwa.2017.05.016

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)
https://doi.org/10.1142/S021820251650041X

An a posteriori-driven adaptive Mixed High-Order method with application to electrostatics

Daniele A. Di Pietro and Ruben Specogna
Journal of Computational Physics 326 35 (2016)
https://doi.org/10.1016/j.jcp.2016.08.041

Discontinuous Galerkin method with arbitrary polygonal finite elements

J. Jaśkowiec, P. Pluciński and A. Stankiewicz
Finite Elements in Analysis and Design 120 1 (2016)
https://doi.org/10.1016/j.finel.2016.06.004