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:

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

Mixed virtual element methods for elliptic optimal control problems with boundary observations in L2(Γ)

Minghui Yang and Zhaojie Zhou
Applied Numerical Mathematics 203 97 (2024)
https://doi.org/10.1016/j.apnum.2024.05.019

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

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

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

Homogenization of composite materials reinforced with unidirectional fibres with complex curvilinear cross section: a virtual element approach

E. Artioli, G. Elefante, A. Sommariva and M. Vianello
Mathematics in Engineering 6 (4) 510 (2024)
https://doi.org/10.3934/mine.2024021

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 second-order penalty-based node-to-segment contact using the Virtual Element Method

Tiago Fernandes Moherdaui, Alfredo Gay Neto and Peter Wriggers
Finite Elements in Analysis and Design 237 104183 (2024)
https://doi.org/10.1016/j.finel.2024.104183

Weak Galerkin methods for elliptic interface problems on curved polygonal partitions

Dan Li, Chunmei Wang and Shangyou Zhang
Journal of Computational and Applied Mathematics 115982 (2024)
https://doi.org/10.1016/j.cam.2024.115982

Weak Galerkin methods for elliptic interface problems on curved polygonal partitions

Dan Li, Chunmei Wang and Shangyou Zhang
Journal of Computational and Applied Mathematics 450 115995 (2024)
https://doi.org/10.1016/j.cam.2024.115995

An Isoparametric Finite Element Method for Time-fractional Parabolic Equation on 2D Curved Domain

Zhixin Liu, Minghui Song and Hui Liang
Journal of Scientific Computing 99 (3) (2024)
https://doi.org/10.1007/s10915-024-02556-8

A High-Order Shifted Boundary Virtual Element Method for Poisson Equations on 2D Curved Domains

Yongli Hou, Yi Liu and Yanqiu Wang
Journal of Scientific Computing 99 (3) (2024)
https://doi.org/10.1007/s10915-024-02552-y

A Cartesian mesh approach to embedded interface problems using the virtual element method

M. Arrutselvi and Sundararajan Natarajan
Journal of Computational Physics 508 112997 (2024)
https://doi.org/10.1016/j.jcp.2024.112997

The Nonconforming Virtual Element Method with Curved Edges

Lourenço Beirão da Veiga, Yi Liu, Lorenzo Mascotto and Alessandro Russo
Journal of Scientific Computing 99 (1) (2024)
https://doi.org/10.1007/s10915-023-02441-w

Evaluation of Inner Products of Implicitly Defined Finite Element Functions on Multiply Connected Planar Mesh Cells

Jeffrey S. Ovall and Samuel E. Reynolds
SIAM Journal on Scientific Computing 46 (1) A338 (2024)
https://doi.org/10.1137/23M1569332

A virtual element method for the solution of 2D time-harmonic elastic wave equations via scalar potentials

Silvia Falletta, Matteo Ferrari and Letizia Scuderi
Journal of Computational and Applied Mathematics 441 115625 (2024)
https://doi.org/10.1016/j.cam.2023.115625

Stabilization-free serendipity virtual element method for plane elasticity

Alvin Chen and N. Sukumar
Computer Methods in Applied Mechanics and Engineering 404 115784 (2023)
https://doi.org/10.1016/j.cma.2022.115784

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

CVEM-BEM Coupling for the Simulation of Time-Domain Wave Fields Scattered by Obstacles with Complex Geometries

Luca Desiderio, Silvia Falletta, Matteo Ferrari and Letizia Scuderi
Computational Methods in Applied Mathematics 23 (2) 353 (2023)
https://doi.org/10.1515/cmam-2022-0084

Nonconforming virtual element discretization for the transmission eigenvalue problem

Dibyendu Adak, David Mora and Iván Velásquez
Computers & Mathematics with Applications 152 250 (2023)
https://doi.org/10.1016/j.camwa.2023.10.032

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

Convergence analysis of expanded mixed virtual element methods for nonlocal problems

Dibyendu Adak
Numerical Methods for Partial Differential Equations 39 (4) 3246 (2023)
https://doi.org/10.1002/num.23007

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

Weak Galerkin finite element method for second order problems on curvilinear polytopal meshes with Lipschitz continuous edges or faces

Qingguang Guan, Gillian Queisser and Wenju Zhao
Computers & Mathematics with Applications 148 282 (2023)
https://doi.org/10.1016/j.camwa.2023.08.017

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

Virtual elements for sound propagation in complex poroelastic media

Abhilash Sreekumar, Savvas P. Triantafyllou and Fabien Chevillotte
Computational Mechanics 69 (1) 347 (2022)
https://doi.org/10.1007/s00466-021-02078-2

Sharper Error Estimates for Virtual Elements and a Bubble-Enriched Version

L. Beira͂o da Veiga and G. Vacca
SIAM Journal on Numerical Analysis 60 (4) 1853 (2022)
https://doi.org/10.1137/21M1411275

Virtual element method on polyhedral meshes for bi-harmonic eigenvalues problems

Franco Dassi and Iván Velásquez
Computers & Mathematics with Applications 121 85 (2022)
https://doi.org/10.1016/j.camwa.2022.07.001

Weakly imposed Dirichlet boundary conditions for 2D and 3D Virtual Elements

Silvia Bertoluzza, Micol Pennacchio and Daniele Prada
Computer Methods in Applied Mechanics and Engineering 400 115454 (2022)
https://doi.org/10.1016/j.cma.2022.115454

Bend 3d mixed virtual element method for Darcy problems

Franco Dassi, Alessio Fumagalli, Anna Scotti and Giuseppe Vacca
Computers & Mathematics with Applications 119 1 (2022)
https://doi.org/10.1016/j.camwa.2022.05.023

Pressure-independent velocity error estimates for (Navier-)Stokes nonconforming virtual element discretization with divergence free

Xin Liu and Yufeng Nie
Numerical Algorithms 90 (2) 477 (2022)
https://doi.org/10.1007/s11075-021-01195-6

A new approach for solving heat conduction under zero and non-zero initial conditions

Cibele Cornejo Jacinto, António Tadeu and Luiz Alkimin de Lacerda
Engineering Analysis with Boundary Elements 144 185 (2022)
https://doi.org/10.1016/j.enganabound.2022.08.015

CVEM-BEM Coupling with Decoupled Orders for 2D Exterior Poisson Problems

Luca Desiderio, Silvia Falletta, Matteo Ferrari and Letizia Scuderi
Journal of Scientific Computing 92 (3) (2022)
https://doi.org/10.1007/s10915-022-01951-3

Virtual element method with adaptive refinement for problems of two-dimensional complex topology models from an engineering perspective

Xiaoxiao Du, Wei Wang, Gang Zhao, et al.
Computational Mechanics 70 (3) 581 (2022)
https://doi.org/10.1007/s00466-022-02179-6

The Virtual Element Method and its Applications

Lourenço Beirão da Veiga and Giuseppe Vacca
SEMA SIMAI Springer Series, The Virtual Element Method and its Applications 31 185 (2022)
https://doi.org/10.1007/978-3-030-95319-5_5

Virtual element methods for general linear elliptic interface problems on polygonal meshes with small edges

Jai Tushar, Anil Kumar and Sarvesh Kumar
Computers & Mathematics with Applications 122 61 (2022)
https://doi.org/10.1016/j.camwa.2022.07.016

Quadrature for implicitly-defined finite element functions on curvilinear polygons

Jeffrey S. Ovall and Samuel E. Reynolds
Computers & Mathematics with Applications 107 1 (2022)
https://doi.org/10.1016/j.camwa.2021.12.003

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

On the Coupling of the Curved Virtual Element Method with the One-Equation Boundary Element Method for 2D Exterior Helmholtz Problems

Luca Desiderio, Silvia Falletta, Matteo Ferrari and Letizia Scuderi
SIAM Journal on Numerical Analysis 60 (4) 2099 (2022)
https://doi.org/10.1137/21M1460776

The Virtual Element Method and its Applications

Peter Wriggers, Fadi Aldakheel and Blaž Hudobivnik
SEMA SIMAI Springer Series, The Virtual Element Method and its Applications 31 557 (2022)
https://doi.org/10.1007/978-3-030-95319-5_13

Solving of multi-connected curvilinear boundary value problems by the fast PIES

Andrzej Kużelewski and Eugeniusz Zieniuk
Computer Methods in Applied Mechanics and Engineering 391 114618 (2022)
https://doi.org/10.1016/j.cma.2022.114618

Immersed Virtual Element Methods for Elliptic Interface Problems in Two Dimensions

Shuhao Cao, Long Chen, Ruchi Guo and Frank Lin
Journal of Scientific Computing 93 (1) (2022)
https://doi.org/10.1007/s10915-022-01949-x

A Virtual Element Method for the Wave Equation on Curved Edges in Two Dimensions

Franco Dassi, Alessio Fumagalli, Ilario Mazzieri, Anna Scotti and Giuseppe Vacca
Journal of Scientific Computing 90 (1) (2022)
https://doi.org/10.1007/s10915-021-01683-w

NURBS Enhanced Virtual Element Methods for the Spatial Discretization of the Multigroup Neutron Diffusion Equation on Curvilinear Polygonal Meshes

J. A. Ferguson, J. Kópházi and M. D. Eaton
Journal of Computational and Theoretical Transport 51 (4) 145 (2022)
https://doi.org/10.1080/23324309.2022.2103150

A Virtual Element Method coupled with a Boundary Integral Non Reflecting condition for 2D exterior Helmholtz problems

L. Desiderio, S. Falletta and L. Scuderi
Computers & Mathematics with Applications 84 296 (2021)
https://doi.org/10.1016/j.camwa.2021.01.002

Hybrid mimetic finite-difference and virtual element formulation for coupled poromechanics

Andrea Borio, François P. Hamon, Nicola Castelletto, Joshua A. White and Randolph R. Settgast
Computer Methods in Applied Mechanics and Engineering 383 113917 (2021)
https://doi.org/10.1016/j.cma.2021.113917

Bulk-surface virtual element method for systems of PDEs in two-space dimensions

Massimo Frittelli, Anotida Madzvamuse and Ivonne Sgura
Numerische Mathematik 147 (2) 305 (2021)
https://doi.org/10.1007/s00211-020-01167-3

NURBS-based geometries: A mapping approach for virtual serendipity elements

Peter Wriggers, Blaž Hudobivnik and Fadi Aldakheel
Computer Methods in Applied Mechanics and Engineering 378 113732 (2021)
https://doi.org/10.1016/j.cma.2021.113732

Polyhedral Methods in Geosciences

Paola F. Antonietti, Chiara Facciolà, Paul Houston, et al.
SEMA SIMAI Springer Series, Polyhedral Methods in Geosciences 27 159 (2021)
https://doi.org/10.1007/978-3-030-69363-3_5

The mixed virtual element method on curved edges in two dimensions

Franco Dassi, Alessio Fumagalli, Davide Losapio, et al.
Computer Methods in Applied Mechanics and Engineering 386 114098 (2021)
https://doi.org/10.1016/j.cma.2021.114098

A virtual element method for the miscible displacement of incompressible fluids in porous media

L. Beirão da Veiga, A. Pichler and G. Vacca
Computer Methods in Applied Mechanics and Engineering 375 113649 (2021)
https://doi.org/10.1016/j.cma.2020.113649

A hybrid virtual–boundary element formulation for heterogeneous materials

Marco Lo Cascio, Alberto Milazzo and Ivano Benedetti
International Journal of Mechanical Sciences 199 106404 (2021)
https://doi.org/10.1016/j.ijmecsci.2021.106404

The FMM accelerated PIES with the modified binary tree in solving potential problems for the domains with curvilinear boundaries

Andrzej Kużelewski and Eugeniusz Zieniuk
Numerical Algorithms 88 (3) 1025 (2021)
https://doi.org/10.1007/s11075-020-01066-6

Scaled boundary cubature scheme for numerical integration over planar regions with affine and curved boundaries

Eric B. Chin and N. Sukumar
Computer Methods in Applied Mechanics and Engineering 380 113796 (2021)
https://doi.org/10.1016/j.cma.2021.113796

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)
https://doi.org/10.1016/j.anucene.2020.107884

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)
https://doi.org/10.1016/j.cma.2020.113543

Virtual Element Method for Solving an Inhomogeneous Brusselator Model With and Without Cross-Diffusion in Pattern Formation

Mehdi Dehghan and Zeinab Gharibi
Journal of Scientific Computing 89 (1) (2021)
https://doi.org/10.1007/s10915-021-01626-5

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)
https://doi.org/10.1016/j.cpc.2019.106870

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

Virtual element method and permanent magnet simulations: potential and mixed formulations

Franco Dassi, Paolo Di Barba and Alessandro Russo
IET Science, Measurement & Technology 14 (10) 1098 (2020)
https://doi.org/10.1049/iet-smt.2020.0322

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)
https://doi.org/10.1016/j.apnum.2019.04.005

Curvilinear virtual elements for contact mechanics

Fadi Aldakheel, Blaž Hudobivnik, Edoardo Artioli, Lourenço Beirão da Veiga and Peter Wriggers
Computer Methods in Applied Mechanics and Engineering 372 113394 (2020)
https://doi.org/10.1016/j.cma.2020.113394

Efficient multi-material continuum topology optimization considering hyperelasticity: Achieving local feature control through regional constraints

Xiaojia Shelly Zhang and Heng Chi
Mechanics Research Communications 105 103494 (2020)
https://doi.org/10.1016/j.mechrescom.2020.103494

Curvilinear Virtual Elements for 2D solid mechanics applications

E. Artioli, L. Beirão da Veiga and F. Dassi
Computer Methods in Applied Mechanics and Engineering 359 112667 (2020)
https://doi.org/10.1016/j.cma.2019.112667

The fast parametric integral equations system in an acceleration of solving polygonal potential boundary value problems

Andrzej Kużelewski and Eugeniusz Zieniuk
Advances in Engineering Software 141 102770 (2020)
https://doi.org/10.1016/j.advengsoft.2020.102770

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)
https://doi.org/10.1142/S0218202520500311

Trefftz Finite Elements on Curvilinear Polygons

Akash Anand, Jeffrey S. Ovall, Samuel E. Reynolds and Steffen Weißer
SIAM Journal on Scientific Computing 42 (2) A1289 (2020)
https://doi.org/10.1137/19M1294046

Modeling curved interfaces without element‐partitioning in the extended finite element method

Eric B. Chin and N. Sukumar
International Journal for Numerical Methods in Engineering 120 (5) 607 (2019)
https://doi.org/10.1002/nme.6150