EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues ESAIM: M2AN, 51 2 (2017) 509-535 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:

Divergence-free stabilized virtual element method for the unsteady incompressible Navier–Stokes problem

Yang Li, Minfu Feng and Yanhong Bai
Journal of Computational and Applied Mathematics 473 116838 (2026)
https://doi.org/10.1016/j.cam.2025.116838

Robust Virtual Element Methods for Coupled Stress-Assisted Diffusion Problems

Rekha Khot, Andrés E. Rubiano and Ricardo Ruiz-Baier
SIAM Journal on Scientific Computing 47 (1) A497 (2025)
https://doi.org/10.1137/24M163640X

A Priori Error Estimate for H1$$ {H}^1 $$ Galerkin Mixed Virtual Element Discretization of Parabolic Equations

Fengxin Chen, Minghui Yang and Zhaojie Zhou
Numerical Methods for Partial Differential Equations 41 (3) (2025)
https://doi.org/10.1002/num.70007

A Nitsche’s Extended Conforming Virtual Element Method for Stokes Interface Problems

Yuxiang Huang, Jinru Chen and Feng Wang
Journal of Scientific Computing 102 (1) (2025)
https://doi.org/10.1007/s10915-024-02746-4

Convergence Analysis of a Nonconforming Virtual Element Method for Compressible Miscible Displacement Problems in Porous Media

Sarvesh Kumar and Devika Shylaja
Numerical Methods for Partial Differential Equations 41 (1) (2025)
https://doi.org/10.1002/num.23162

Optimal convergence analysis of the lowest-order nonconforming virtual element method for general nonlinear parabolic equations

Yanping Chen, Wanxiang Liu, Yang Wang and Huaming Yi
Journal of Computational and Applied Mathematics 465 116576 (2025)
https://doi.org/10.1016/j.cam.2025.116576

A virtual element method for a convective Brinkman-Forchheimer problem coupled with a heat equation

Danilo Amigo, Felipe Lepe, Enrique Otárola and Gonzalo Rivera
Computers & Mathematics with Applications 191 1 (2025)
https://doi.org/10.1016/j.camwa.2025.04.015

Nonconforming virtual element method for an incompressible miscible displacement problem in porous media

Sarvesh Kumar and Devika Shylaja
Computers & Mathematics with Applications 183 153 (2025)
https://doi.org/10.1016/j.camwa.2025.01.021

Mixed Virtual Element Approximation for the Five-Field Formulation of the Steady Boussinesq Problem with Temperature-Dependent Parameters

Zeinab Gharibi
Journal of Scientific Computing 102 (1) (2025)
https://doi.org/10.1007/s10915-024-02722-y

A lowest-order divergence-free virtual element method for Navier-Stokes equations with damping on polygonal mesh

Yanping Chen, Qing Li, Jian Huang and Yu Xiong
Journal of Mathematical Analysis and Applications 552 (2) 129792 (2025)
https://doi.org/10.1016/j.jmaa.2025.129792

An arbitrary-order Virtual Element Method for the Helmholtz equation applied to wave field calculation in port

Ronan Dupont
Results in Applied Mathematics 26 100598 (2025)
https://doi.org/10.1016/j.rinam.2025.100598

Optimal convergence analysis of an energy dissipation property virtual element method for the nonlinear Benjamin-Bona-Mahony-Burgers equation

Yanping Chen, Wanxiang Liu, Fangfang Qin and Qin Liang
Computers & Mathematics with Applications 192 37 (2025)
https://doi.org/10.1016/j.camwa.2025.05.003

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

A Fractional PDE-Based Model for Nerve Impulse Transport Solved Using a Conforming Virtual Element Method: Application to Prosthetic Implants

Zaffar Mehdi Dar, Chandru Muthusamy and Higinio Ramos
Axioms 14 (6) 398 (2025)
https://doi.org/10.3390/axioms14060398

A High-Order Dual Robust Virtual Element Method for the Inductionless Magnetohydrodynamic Equations

Xianghai Zhou, Haiyan Su and Xinlong Feng
Journal of Scientific Computing 103 (2) (2025)
https://doi.org/10.1007/s10915-025-02875-4

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

Virtual element approximations of the time-fractional nonlinear convection-diffusion equation on polygonal meshes

Zaffar Mehdi Dar, M. Arrutselvi, Chandru Muthusamy, Sundararajan Natarajan and Gianmarco Manzini
Mathematics in Engineering 7 (2) 96 (2025)
https://doi.org/10.3934/mine.2025005

A Medius Error Analysis for Interior Penalty Virtual Element Method for the Biharmonic Problem

Jikun Zhao, Haofei Jian, Wenhao Zhu and Bei Zhang
Journal of Scientific Computing 103 (1) (2025)
https://doi.org/10.1007/s10915-025-02827-y

A noncoforming virtual element approximation for the Oseen eigenvalue problem

Dibyendu Adak, Felipe Lepe and Gonzalo Rivera
IMA Journal of Numerical Analysis (2025)
https://doi.org/10.1093/imanum/drae108

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

Reduced basis stabilization and post-processing for the virtual element method

Fabio Credali, Silvia Bertoluzza and Daniele Prada
Computer Methods in Applied Mechanics and Engineering 420 116693 (2024)
https://doi.org/10.1016/j.cma.2023.116693

A unified local projection-based stabilized virtual element method for the coupled Stokes-Darcy problem

Sudheer Mishra and E. Natarajan
Advances in Computational Mathematics 50 (6) (2024)
https://doi.org/10.1007/s10444-024-10199-4

The Hermite-type virtual element method for second order problem

Jikun Zhao, Fengchen Zhou, Bei Zhang and Xiaojing Dong
Computers & Mathematics with Applications 172 70 (2024)
https://doi.org/10.1016/j.camwa.2024.07.028

A linearized BDF2 virtual element method for the unsteady Brinkman–Forchheimer equations with variable time step

Yanping Chen and Yu Xiong
Chaos, Solitons & Fractals 187 115415 (2024)
https://doi.org/10.1016/j.chaos.2024.115415

A fully mixed virtual element method for Darcy–Forchheimer miscible displacement of incompressible fluids appearing in porous media

Mehdi Dehghan and Zeinab Gharibi
IMA Journal of Numerical Analysis 44 (2) 797 (2024)
https://doi.org/10.1093/imanum/drad023

Unconditional error analysis of linearized BDF2 mixed virtual element method for semilinear parabolic problems on polygonal meshes

Wanxiang Liu, Yanping Chen, Jianwei Zhou and Qin Liang
Journal of Computational and Applied Mathematics 446 115864 (2024)
https://doi.org/10.1016/j.cam.2024.115864

A Framework for Implementing General Virtual Element Spaces

Andreas Dedner and Alice Hodson
SIAM Journal on Scientific Computing 46 (3) B229 (2024)
https://doi.org/10.1137/23M1573653

The virtual element method with interior penalty for the fourth-order singular perturbation problem

Bei Zhang and Jikun Zhao
Communications in Nonlinear Science and Numerical Simulation 133 107964 (2024)
https://doi.org/10.1016/j.cnsns.2024.107964

On stabilized equal-order virtual element methods for the Navier-Stokes equations on polygonal meshes

Yang Li, Chaolang Hu and Minfu Feng
Computers & Mathematics with Applications 154 267 (2024)
https://doi.org/10.1016/j.camwa.2023.11.031

An enriched virtual element method for 2D‐3C generalized membrane shell model on surface

Qian Yang, Xiaoqin Shen, Jikun Zhao and Yumin Cheng
International Journal for Numerical Methods in Engineering 125 (8) (2024)
https://doi.org/10.1002/nme.7432

A Banach spaces-based fully mixed virtual element method for the stationary two-dimensional Boussinesq equations

Gabriel N. Gatica and Zeinab Gharibi
Journal of Computational and Applied Mathematics 447 115885 (2024)
https://doi.org/10.1016/j.cam.2024.115885

The Hermite-type virtual element method with interior penalty for the fourth-order elliptic problem

Jikun Zhao, Teng Chen, Bei Zhang and Xiaojing Dong
Calcolo 61 (1) (2024)
https://doi.org/10.1007/s10092-023-00555-z

A Virtual Element method for non-Newtonian pseudoplastic Stokes flows

Paola F. Antonietti, Lourenço Beirão da Veiga, Michele Botti, Giuseppe Vacca and Marco Verani
Computer Methods in Applied Mechanics and Engineering 428 117079 (2024)
https://doi.org/10.1016/j.cma.2024.117079

Numerical Solution of the Biot/Elasticity Interface Problem Using Virtual Element Methods

Sarvesh Kumar, David Mora, Ricardo Ruiz-Baier and Nitesh Verma
Journal of Scientific Computing 98 (3) (2024)
https://doi.org/10.1007/s10915-023-02444-7

BDDC Preconditioners for Virtual Element Approximations of the Three-Dimensional Stokes Equations

Tommaso Bevilacqua, Franco Dassi, Stefano Zampini and Simone Scacchi
SIAM Journal on Scientific Computing 46 (1) A156 (2024)
https://doi.org/10.1137/23M1567679

The nonconforming virtual element method for optimal control problem governed by Stokes equations

Chongna Sun, Minghui Yang and Zhaojie Zhou
Journal of Applied Mathematics and Computing 70 (3) 2019 (2024)
https://doi.org/10.1007/s12190-024-02035-1

Mixed Virtual Element approximation of linear acoustic wave equation

Franco Dassi, Alessio Fumagalli, Ilario Mazzieri and Giuseppe Vacca
IMA Journal of Numerical Analysis 44 (5) 2864 (2024)
https://doi.org/10.1093/imanum/drad078

A mixed virtual element method for the two-dimensional Navier-Stokes equations in stream-function formulation

Xi Zhang and Minfu Feng
Computers & Mathematics with Applications 175 119 (2024)
https://doi.org/10.1016/j.camwa.2024.09.020

An analysis of nonconforming virtual element methods on polytopal meshes with small faces

Hyeokjoo Park and Do Y. Kwak
Mathematical Models and Methods in Applied Sciences 34 (04) 571 (2024)
https://doi.org/10.1142/S021820252450009X

Numerical integration in the virtual element method with the scaled boundary cubature scheme

Eric B. Chin, Franco Dassi, Gianmarco Manzini and N. Sukumar
International Journal for Numerical Methods in Engineering 125 (20) (2024)
https://doi.org/10.1002/nme.7549

The virtual element method on polygonal pixel–based tessellations

S. Bertoluzza, M. Montardini, M. Pennacchio and D. Prada
Journal of Computational Physics 518 113334 (2024)
https://doi.org/10.1016/j.jcp.2024.113334

The stabilized nonconforming virtual element method for the Darcy–Stokes problem

Jikun Zhao, Wenhao Zhu, Bei Zhang and Yongqin Yang
Communications in Nonlinear Science and Numerical Simulation 138 108252 (2024)
https://doi.org/10.1016/j.cnsns.2024.108252

H1-conforming virtual element method for the Laplacian eigenvalue problem in mixed form

Jian Meng, Liquan Mei and Mingfa Fei
Journal of Computational and Applied Mathematics 436 115395 (2024)
https://doi.org/10.1016/j.cam.2023.115395

Curved Domains in Magnetics: A Virtual Element Method Approach for the T.E.A.M. 25 Benchmark Problem

Franco Dassi, Paolo Di Barba and Alessandro Russo
Electronics 13 (11) 2053 (2024)
https://doi.org/10.3390/electronics13112053

A stabilized Crank-Nicolson virtual element method for the unsteady Navier-Stokes problems with high Reynolds number

Yang Li, Yanhong Bai and Minfu Feng
Numerical Algorithms 96 (4) 1779 (2024)
https://doi.org/10.1007/s11075-023-01685-9

Unconditionally stable small stencil enriched multiple point flux approximations of heterogeneous diffusion problems on general meshes

Julien Coatléven
IMA Journal of Numerical Analysis 44 (6) 3435 (2024)
https://doi.org/10.1093/imanum/drad087

Virtual element discretization method to optimal control problem governed by Stokes equations with pointwise control constraint on arbitrary polygonal meshes

Yanwei Li, Huipo Liu and Zhaojie Zhou
Journal of Computational and Applied Mathematics 450 116002 (2024)
https://doi.org/10.1016/j.cam.2024.116002

Inf–sup stabilized Scott–Vogelius pairs on general shape-regular simplicial grids by Raviart–Thomas enrichment

Volker John, Xu Li, Christian Merdon and Hongxing Rui
Mathematical Models and Methods in Applied Sciences 34 (05) 919 (2024)
https://doi.org/10.1142/S0218202524500180

Analysis of divergence free conforming virtual elements for the Brinkman problem

Xuehai Huang and Feng Wang
Mathematical Models and Methods in Applied Sciences 33 (06) 1245 (2023)
https://doi.org/10.1142/S021820252350029X

Mixed virtual element method for the Helmholtz transmission eigenvalue problem on polytopal meshes

Jian Meng, Gang Wang and Liquan Mei
IMA Journal of Numerical Analysis 43 (3) 1685 (2023)
https://doi.org/10.1093/imanum/drac019

A nonconforming immersed virtual element method for elliptic interface problems

Hyeokjoo Park and Do Young Kwak
ESAIM: Mathematical Modelling and Numerical Analysis 57 (6) 3615 (2023)
https://doi.org/10.1051/m2an/2023078

The virtual element method for a 2D incompressible MHD system

S. Naranjo-Alvarez, L. Beirão da Veiga, V.A. Bokil, F. Dassi, V. Gyrya and G. Manzini
Mathematics and Computers in Simulation 211 301 (2023)
https://doi.org/10.1016/j.matcom.2023.03.029

Virtual element method for elliptic bulk‐surface PDEs in three space dimensions

Massimo Frittelli, Anotida Madzvamuse and Ivonne Sgura
Numerical Methods for Partial Differential Equations 39 (6) 4221 (2023)
https://doi.org/10.1002/num.23040

A Conforming Virtual Element Method Based on Unfitted Meshes for the Elliptic Interface Problem

Haimei Wang, Feng Wang, Jinru Chen and Haifeng Ji
Journal of Scientific Computing 96 (1) (2023)
https://doi.org/10.1007/s10915-023-02229-y

The nonconforming locking-free virtual element method for the Biot's consolidation model in poroelasticity

Hao Liang and Hongxing Rui
Computers & Mathematics with Applications 148 269 (2023)
https://doi.org/10.1016/j.camwa.2023.08.012

Stability and Interpolation Properties for Stokes-Like Virtual Element Spaces

Jian Meng, Lourenço Beirão da Veiga and Lorenzo Mascotto
Journal of Scientific Computing 94 (3) (2023)
https://doi.org/10.1007/s10915-023-02112-w

Adaptive Virtual Element Method for Optimal Control Problem Governed by Stokes Equations

Yanwei Li, Qiming Wang and Zhaojie Zhou
Journal of Scientific Computing 97 (3) (2023)
https://doi.org/10.1007/s10915-023-02377-1

Virtual element method for nonlinear Sobolev equation on polygonal meshes

Wanxiang Liu, Yanping Chen, Qiling Gu and Yunqing Huang
Numerical Algorithms 94 (4) 1731 (2023)
https://doi.org/10.1007/s11075-023-01553-6

Error estimates for a vorticity-based velocity–stress formulation of the Stokes eigenvalue problem

Felipe Lepe, Gonzalo Rivera and Jesus Vellojin
Journal of Computational and Applied Mathematics 420 114798 (2023)
https://doi.org/10.1016/j.cam.2022.114798

Nonconforming virtual element methods for the fourth-order variational inequalities of the first kind

Jiali Qiu, Jikun Zhao and Fei Wang
Journal of Computational and Applied Mathematics 425 115025 (2023)
https://doi.org/10.1016/j.cam.2022.115025

Unconditional error analysis of a linearized BDF2 virtual element method for nonlinear Ginzburg–Landau equation with variable time step

Nan Wang and Meng Li
Communications in Nonlinear Science and Numerical Simulation 116 106889 (2023)
https://doi.org/10.1016/j.cnsns.2022.106889

A new class of stabilized virtual element methods for the time-dependent Oseen equations

Yanhong Bai, Yang Li and Minfu Feng
Computers & Mathematics with Applications 145 303 (2023)
https://doi.org/10.1016/j.camwa.2023.06.041

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

An arbitrary-order fully discrete Stokes complex on general polyhedral meshes

Marien-Lorenzo Hanot
Mathematics of Computation 92 (343) 1977 (2023)
https://doi.org/10.1090/mcom/3837

VIRTUAL ELEMENT APPROXIMATIONS FOR NON-STATIONARY NAVIER-STOKES EQUATIONS ON POLYGONAL MESHES

Nitesh Verma and Sarvesh Kumar
Journal of Applied Analysis & Computation 13 (3) 1155 (2023)
https://doi.org/10.11948/20210381

Optimal Error Estimates of Coupled and Divergence-Free Virtual Element Methods for the Poisson–Nernst–Planck/Navier–Stokes Equations and Applications in Electrochemical Systems

Mehdi Dehghan, Zeinab Gharibi and Ricardo Ruiz-Baier
Journal of Scientific Computing 94 (3) (2023)
https://doi.org/10.1007/s10915-023-02126-4

Dissipative nonconforming virtual element method for the fourth order nonlinear extended Fisher-Kolmogorov equation

Lifang Pei, Chaofeng Zhang and Meng Li
Computers & Mathematics with Applications 152 28 (2023)
https://doi.org/10.1016/j.camwa.2023.10.007

Virtual element method for the Navier–Stokes equation coupled with the heat equation

Paola F Antonietti, Giuseppe Vacca and Marco Verani
IMA Journal of Numerical Analysis 43 (6) 3396 (2023)
https://doi.org/10.1093/imanum/drac072

The interior penalty virtual element method for the biharmonic problem

Jikun Zhao, Shipeng Mao, Bei Zhang and Fei Wang
Mathematics of Computation 92 (342) 1543 (2023)
https://doi.org/10.1090/mcom/3828

The divergence‐free nonconforming virtual element method for the Navier–Stokes problem

Bei Zhang, Jikun Zhao and Meng Li
Numerical Methods for Partial Differential Equations 39 (3) 1977 (2023)
https://doi.org/10.1002/num.22812

A pressure‐robust weak Galerkin finite element method for Navier–Stokes equations

Lin Mu
Numerical Methods for Partial Differential Equations 39 (3) 2327 (2023)
https://doi.org/10.1002/num.22969

A stabilized divergence-free virtual element scheme for the nematic liquid crystal flows

Xuyang Wang, Guang-an Zou and Bo Wang
Applied Numerical Mathematics 192 104 (2023)
https://doi.org/10.1016/j.apnum.2023.06.004

The virtual element method for the 3D resistive magnetohydrodynamic model

Lourenço Beirão da Veiga, Franco Dassi, Gianmarci Manzini and Lorenzo Mascotto
Mathematical Models and Methods in Applied Sciences 33 (03) 643 (2023)
https://doi.org/10.1142/S021820252350015X

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

An extrapolated Crank-Nicolson virtual element scheme for the nematic liquid crystal flows

Guang-an Zou, Xuyang Wang and Jian Li
Advances in Computational Mathematics 49 (3) (2023)
https://doi.org/10.1007/s10444-023-10028-0

A Morley-type virtual element approximation for a wind-driven ocean circulation model on polygonal meshes

D. Adak, D. Mora and A. Silgado
Journal of Computational and Applied Mathematics 425 115026 (2023)
https://doi.org/10.1016/j.cam.2022.115026

The nonconforming virtual element method for Oseen’s equation using a stream-function formulation

Dibyendu Adak and Gianmarco Manzini
ESAIM: Mathematical Modelling and Numerical Analysis 57 (6) 3303 (2023)
https://doi.org/10.1051/m2an/2023075

Theoretical analysis and construction of numerical method for solving the Navier–Stokes equations in rotation form with corner singularity

Viktor A. Rukavishnikov and Alexey V. Rukavishnikov
Journal of Computational and Applied Mathematics 429 115218 (2023)
https://doi.org/10.1016/j.cam.2023.115218

A pressure-robust virtual element method for the Navier-Stokes problem on polygonal mesh

Ying Wang, Gang Wang and Yue Shen
Computers & Mathematics with Applications 131 124 (2023)
https://doi.org/10.1016/j.camwa.2022.12.013