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 Priori and a Posteriori Error Analyses of a Pressure-Robust Virtual Element Method for the Two-Dimensional Brinkman problem

Yu Xiong, Yanping Chen, Jianwei Zhou, Yanping Zhou and Jian Huang
Journal of Scientific Computing 106 (2) (2026)
https://doi.org/10.1007/s10915-026-03186-y

Analysis of an SUPG-stabilized virtual element method for scalar hyperbolic equations

Mathias Dauphin and Giuseppe Vacca
Computer Methods in Applied Mechanics and Engineering 448 118441 (2026)
https://doi.org/10.1016/j.cma.2025.118441

C1−C0 Conforming virtual element approximations for sixth-order problems

Luis Pérez, Carlos Reales, Alberth Silgado and Iván Velásquez
Journal of Computational Physics 545 114483 (2026)
https://doi.org/10.1016/j.jcp.2025.114483

A virtual element method for the Biot-Brinkman equations using Nitsche’s technique

David Mora, Jesus Vellojin and Nitesh Verma
Computer Methods in Applied Mechanics and Engineering 448 118447 (2026)
https://doi.org/10.1016/j.cma.2025.118447

A noncoforming virtual element approximation for the Oseen eigenvalue problem

Dibyendu Adak, Felipe Lepe and Gonzalo Rivera
IMA Journal of Numerical Analysis 46 (1) 299 (2026)
https://doi.org/10.1093/imanum/drae108

A unified stabilized virtual element method for the generalized Oseen equation: stability and robustness

Sudheer Mishra and E. Natarajan
Journal of Scientific Computing 106 (1) (2026)
https://doi.org/10.1007/s10915-025-03162-y

Fully-discrete virtual element method with exact stress symmetry for the viscoelasticity problem on polygonal meshes

Gang Wang, Ying Wang, Xiaojing Dong and Yinnian He
Communications in Nonlinear Science and Numerical Simulation 152 109372 (2026)
https://doi.org/10.1016/j.cnsns.2025.109372

The Arrow-Hurwicz Iteration for Virtual Element Discretizations of the Incompressible Navier-Stokes Equations

Binbin Du, Shenxiang Cheng, Yue Yu and Chuanjun Chen
Journal of Scientific Computing 106 (2) (2026)
https://doi.org/10.1007/s10915-026-03194-y

POLYDIM: A C++ library for POLYtopal DIscretization Methods

Stefano Berrone, Andrea Borio, Gioana Teora and Fabio Vicini
Computer Physics Communications 320 109937 (2026)
https://doi.org/10.1016/j.cpc.2025.109937

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

The Lowest-Order Stabilized Virtual Element Method for the Evolutionary Navier-Stokes Equations with Small Viscosity

Xin Liu, Qixuan Song, Rui Zhang and Zhangxin Chen
Journal of Scientific Computing 106 (2) (2026)
https://doi.org/10.1007/s10915-026-03181-3

Analysis and virtual element discretisation of a Stokes/Biot–Kirchhoff bulk–surface model

Franco Dassi, Rekha Khot, Andrés E. Rubiano and Ricardo Ruiz-Baier
Computer Methods in Applied Mechanics and Engineering 449 118545 (2026)
https://doi.org/10.1016/j.cma.2025.118545

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

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

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

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

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

An equal-order virtual element framework for the coupled Stokes-Temperature equation with nonlinear viscosity

Sudheer Mishra and E Natarajan
Journal of Scientific Computing 104 (2) (2025)
https://doi.org/10.1007/s10915-025-02986-y

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 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

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 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

A virtual element method with IMEX-SAV scheme for the incompressible magnetohydrodynamics equations

Xiaojing Dong, Yunqing Huang and Tianwen Wang
IMA Journal of Numerical Analysis (2025)
https://doi.org/10.1093/imanum/draf105

Three parameter-robust virtual element numerical schemes for a Stokes–Biot fluid-poroelastic structure interaction model

Xin Liu, Qixuan Song, Yiqiang Li and Junfeng Zhao
ESAIM: Mathematical Modelling and Numerical Analysis 59 (4) 2111 (2025)
https://doi.org/10.1051/m2an/2025055

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

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

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

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

Nitsche’s serendipity virtual element method for the eigenvalue problem

Jian Meng, Xu Qian, Fang Su and Bing-Bing Xu
Computer Methods in Applied Mechanics and Engineering 446 118336 (2025)
https://doi.org/10.1016/j.cma.2025.118336

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 pressure-robust lowest-order virtual element method for the natural convection problem on general mesh

Sisi Liang, Haiyan Su and Xinlong Feng
Computers & Mathematics with Applications 197 295 (2025)
https://doi.org/10.1016/j.camwa.2025.09.010

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

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 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

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

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

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

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

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

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

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

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

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 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

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

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 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

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

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

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

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

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

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

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

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

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

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

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

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 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

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

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

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 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

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

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

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

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

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

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

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 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 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

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

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 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

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