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):

Virtual Elements for the Reissner-Mindlin plate problem

Claudia Chinosi
Numerical Methods for Partial Differential Equations 34 (4) 1117 (2018)
DOI: 10.1002/num.22248
See this article

Some aspects on the computational implementation of diverse terms arising in mixed virtual element formulations

Filánder A. Sequeira and Helen Guillén-Oviedo
Numerical Algorithms (2021)
DOI: 10.1007/s11075-021-01123-8
See this article

A priori error analysis for a mixed VEM discretization of the spectral problem for the Laplacian operator

Felipe Lepe and Gonzalo Rivera
Calcolo 58 (2) (2021)
DOI: 10.1007/s10092-021-00412-x
See this article

Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations

Konstantin Lipnikov and Gianmarco Manzini
Lecture Notes in Computational Science and Engineering, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations 114 311 (2016)
DOI: 10.1007/978-3-319-41640-3_10
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

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 (2021)
DOI: 10.1002/num.22812
See this article

On the locking-free three-field virtual element methods for Biot’s consolidation model in poroelasticity

Xialan Tang, Zhibin Liu, Baiju Zhang and Minfu Feng
ESAIM: Mathematical Modelling and Numerical Analysis 55 S909 (2021)
DOI: 10.1051/m2an/2020064
See this article

A dual hybrid virtual element method for plane elasticity problems

Edoardo Artioli, Stefano de Miranda, Carlo Lovadina and Luca Patruno
ESAIM: Mathematical Modelling and Numerical Analysis 54 (5) 1725 (2020)
DOI: 10.1051/m2an/2020011
See this article

Advances in Computational Plasticity

R. L. Taylor and E. Artioli
Computational Methods in Applied Sciences, Advances in Computational Plasticity 46 381 (2018)
DOI: 10.1007/978-3-319-60885-3_18
See this article

$$H({\text {div}})$$ H ( div ) and $$H(\mathbf{curl})$$ H ( curl ) -conforming virtual element methods

L. Beirão da Veiga, F. Brezzi, L. D. Marini and A. Russo
Numerische Mathematik 133 (2) 303 (2016)
DOI: 10.1007/s00211-015-0746-1
See this article

Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations

Lourenco Beirão da Veiga, Franco Brezzi, Luisa Donatella Marini and Alessandro Russo
Lecture Notes in Computational Science and Engineering, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations 114 39 (2016)
DOI: 10.1007/978-3-319-41640-3_2
See this article

The Virtual Element Method for large scale Discrete Fracture Network simulations: fracture-independent mesh generation

Stefano Berrone, Matìas Fernando Benedetto, Andrea Borio, Sandra Pieraccini and Stefano Scialò
PAMM 15 (1) 19 (2015)
DOI: 10.1002/pamm.201510006
See this article

A mixed virtual element method for the pseudostress–velocity formulation of the Stokes problem

Ernesto Cáceres and Gabriel N. Gatica
IMA Journal of Numerical Analysis 37 (1) 296 (2017)
DOI: 10.1093/imanum/drw002
See this article

Gradient correction for polygonal and polyhedral finite elements

Cameron Talischi, Anderson Pereira, Ivan F. M. Menezes and Glaucio H. Paulino
International Journal for Numerical Methods in Engineering 102 (3-4) 728 (2015)
DOI: 10.1002/nme.4851
See this article

Advances in Discretization Methods

Matías Fernando Benedetto, Stefano Berrone and Andrea Borio
SEMA SIMAI Springer Series, Advances in Discretization Methods 12 167 (2016)
DOI: 10.1007/978-3-319-41246-7_8
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

A low-order locking-free virtual element for linear elasticity problems

Xialan Tang, Zhibin Liu, Baiju Zhang and Minfu Feng
Computers & Mathematics with Applications 80 (5) 1260 (2020)
DOI: 10.1016/j.camwa.2020.04.032
See this article

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)
DOI: 10.1016/j.camwa.2020.06.005
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

Weak Galerkin method for the coupled Darcy–Stokes flow

Wenbin Chen, Fang Wang and Yanqiu Wang
IMA Journal of Numerical Analysis 36 (2) 897 (2016)
DOI: 10.1093/imanum/drv012
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

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

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)
DOI: 10.1016/j.cma.2020.113649
See this article

Stabilized virtual element methods for the unsteady incompressible Navier–Stokes equations

Diego Irisarri and Guillermo Hauke
Calcolo 56 (4) (2019)
DOI: 10.1007/s10092-019-0332-5
See this article

Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshes

Daniele A. Di Pietro and Alexandre Ern
IMA Journal of Numerical Analysis 37 (1) 40 (2017)
DOI: 10.1093/imanum/drw003
See this article

Øystein S. Klemetsdal, Olav Møyner, Xavier Raynaud and Knut-Andreas Lie
323 585 (2020)
DOI: 10.1007/978-3-030-43651-3_55
See this article

Virtual element method for two-dimensional linear elasticity problem in mixed weakly symmetric formulation

Baiju Zhang and Minfu Feng
Applied Mathematics and Computation 328 1 (2018)
DOI: 10.1016/j.amc.2018.01.023
See this article

A virtual element and interface based concurrent multiscale method for failure analysis of quasi brittle heterogeneous composites

F. López Rivarola, N.A. Labanda, M.F. Benedetto and G. Etse
Computers & Structures 239 106338 (2020)
DOI: 10.1016/j.compstruc.2020.106338
See this article

Some basic formulations of the virtual element method (VEM) for finite deformations

H. Chi, L. Beirão da Veiga and G.H. Paulino
Computer Methods in Applied Mechanics and Engineering 318 148 (2017)
DOI: 10.1016/j.cma.2016.12.020
See this article

Basic principles of hp virtual elements on quasiuniform meshes

L. Beir ao da Veiga, A. Chernov, L. Mascotto and A. Russo
Mathematical Models and Methods in Applied Sciences 26 (08) 1567 (2016)
DOI: 10.1142/S021820251650038X
See this article

BEM-based Finite Element Approaches on Polytopal Meshes

Steffen Weißer
Lecture Notes in Computational Science and Engineering, BEM-based Finite Element Approaches on Polytopal Meshes 130 177 (2019)
DOI: 10.1007/978-3-030-20961-2_6
See this article

A lowest-order virtual element method for the Helmholtz transmission eigenvalue problem

Jian Meng, Gang Wang and Liquan Mei
Calcolo 58 (1) (2021)
DOI: 10.1007/s10092-020-00391-5
See this article

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

Gabriel N. Gatica, Mauricio Munar and Filánder A. Sequeira
Calcolo 55 (2) (2018)
DOI: 10.1007/s10092-018-0262-7
See this article

A simple virtual element-based flux recovery on quadtree

Shuhao Cao
Electronic Research Archive (2021)
DOI: 10.3934/era.2021054
See this article

A weak Galerkin finite element method based on H(div) virtual element for Darcy flow on polytopal meshes

Gang Wang, Ying Wang and Yinnian He
Journal of Computational and Applied Mathematics 398 113677 (2021)
DOI: 10.1016/j.cam.2021.113677
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

Advanced computation of steady-state fluid flow in Discrete Fracture-Matrix models: FEM–BEM and VEM–VEM fracture-block coupling

S. Berrone, A. Borio, C. Fidelibus, et al.
GEM - International Journal on Geomathematics 9 (2) 377 (2018)
DOI: 10.1007/s13137-018-0105-3
See this article

A mixed virtual element method for the Brinkman problem

Ernesto Cáceres, Gabriel N. Gatica and Filánder A. Sequeira
Mathematical Models and Methods in Applied Sciences 27 (04) 707 (2017)
DOI: 10.1142/S0218202517500142
See this article

Stability analysis for the virtual element method

Lourenço Beirão da Veiga, Carlo Lovadina and Alessandro Russo
Mathematical Models and Methods in Applied Sciences 27 (13) 2557 (2017)
DOI: 10.1142/S021820251750052X
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

An H1-conforming virtual element for Darcy and Brinkman equations

Giuseppe Vacca
Mathematical Models and Methods in Applied Sciences 28 (01) 159 (2018)
DOI: 10.1142/S0218202518500057
See this article

On the Coupling of VEM and BEM in Two and Three Dimensions

Gabriel N. Gatica and Salim Meddahi
SIAM Journal on Numerical Analysis 57 (6) 2493 (2019)
DOI: 10.1137/18M1202487
See this article

Dual virtual element method in presence of an inclusion

Alessio Fumagalli
Applied Mathematics Letters 86 22 (2018)
DOI: 10.1016/j.aml.2018.06.004
See this article

A virtual element approximation for the pseudostress formulation of the Stokes eigenvalue problem

Felipe Lepe and Gonzalo Rivera
Computer Methods in Applied Mechanics and Engineering 379 113753 (2021)
DOI: 10.1016/j.cma.2021.113753
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

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

Flow simulations in porous media with immersed intersecting fractures

Stefano Berrone, Sandra Pieraccini and Stefano Scialò
Journal of Computational Physics 345 768 (2017)
DOI: 10.1016/j.jcp.2017.05.049
See this article

Virtual element methods for parabolic problems on polygonal meshes

Giuseppe Vacca and Lourenco Beirão da Veiga
Numerical Methods for Partial Differential Equations 31 (6) 2110 (2015)
DOI: 10.1002/num.21982
See this article

Numerical analysis of fully discrete energy stable weak Galerkin finite element Scheme for a coupled Cahn-Hilliard-Navier-Stokes phase-field model

Mehdi Dehghan and Zeinab Gharibi
Applied Mathematics and Computation 410 126487 (2021)
DOI: 10.1016/j.amc.2021.126487
See this article

A note on the devising of superconvergent HDG methods for Stokes flow byM-decompositions

Bernardo Cockburn, Guosheng Fu and Weifeng Qiu
IMA Journal of Numerical Analysis drw029 (2016)
DOI: 10.1093/imanum/drw029
See this article

A least-squares virtual element method for second-order elliptic problems

Ying Wang and Gang Wang
Computers & Mathematics with Applications 80 (8) 1873 (2020)
DOI: 10.1016/j.camwa.2020.08.023
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

A $C^1$ Virtual Element Method for the Cahn--Hilliard Equation with Polygonal Meshes

P. F. Antonietti, L. Beira͂o da Veiga, S. Scacchi and M. Verani
SIAM Journal on Numerical Analysis 54 (1) 34 (2016)
DOI: 10.1137/15M1008117
See this article

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

The nonconforming virtual element method

Blanca Ayuso de Dios, Konstantin Lipnikov and Gianmarco Manzini
ESAIM: Mathematical Modelling and Numerical Analysis 50 (3) 879 (2016)
DOI: 10.1051/m2an/2015090
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 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

Mixed virtual element methods for general second order elliptic problems on polygonal meshes

Lourenço Beirão da Veiga, Franco Brezzi, Luisa Donatella Marini and Alessandro Russo
ESAIM: Mathematical Modelling and Numerical Analysis 50 (3) 727 (2016)
DOI: 10.1051/m2an/2015067
See this article

A mixed virtual element method for the vibration problem of clamped Kirchhoff plate

Jian Meng and Liquan Mei
Advances in Computational Mathematics 46 (5) (2020)
DOI: 10.1007/s10444-020-09810-1
See this article

Arbitrary order 2D virtual elements for polygonal meshes: part II, inelastic problem

E. Artioli, L. Beirão da Veiga, C. Lovadina and E. Sacco
Computational Mechanics 60 (4) 643 (2017)
DOI: 10.1007/s00466-017-1429-9
See this article

Mixed Virtual Elements for discrete fracture network simulations

Matías Fernando Benedetto, Andrea Borio and Stefano Scialò
Finite Elements in Analysis and Design 134 55 (2017)
DOI: 10.1016/j.finel.2017.05.011
See this article

A posteriori error estimates for the one and one-half Dimensional Relativistic Vlasov–Maxwell system

Mohammad Asadzadeh and Christoffer Standar
BIT Numerical Mathematics 58 (1) 5 (2018)
DOI: 10.1007/s10543-017-0666-9
See this article

A stress/displacement Virtual Element method for plane elasticity problems

E. Artioli, S. de Miranda, C. Lovadina and L. Patruno
Computer Methods in Applied Mechanics and Engineering 325 155 (2017)
DOI: 10.1016/j.cma.2017.06.036
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

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 mixed virtual element method for a pseudostress-based formulation of linear elasticity

Ernesto Cáceres, Gabriel N. Gatica and Filánder A. Sequeira
Applied Numerical Mathematics 135 423 (2019)
DOI: 10.1016/j.apnum.2018.09.003
See this article

Comparison of the response to geometrical complexity of methods for unstationary simulations in discrete fracture networks with conforming, polygonal, and non-matching grids

Andrea Borio, Alessio Fumagalli and Stefano Scialò
Computational Geosciences (2020)
DOI: 10.1007/s10596-020-09996-9
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

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 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

A Family of Three-Dimensional Virtual Elements with Applications to Magnetostatics

L. Beira͂o da Veiga, F. Brezzi, F. Dassi, L. D. Marini and A. Russo
SIAM Journal on Numerical Analysis 56 (5) 2940 (2018)
DOI: 10.1137/18M1169886
See this article

Numerical Methods for PDEs

Marc Gerritsma, Artur Palha, Varun Jain and Yi Zhang
SEMA SIMAI Springer Series, Numerical Methods for PDEs 15 31 (2018)
DOI: 10.1007/978-3-319-94676-4_3
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

A mixed virtual element method for the Navier–Stokes equations

Gabriel N. Gatica, Mauricio Munar and Filánder A. Sequeira
Mathematical Models and Methods in Applied Sciences 28 (14) 2719 (2018)
DOI: 10.1142/S0218202518500598
See this article

BEM-based Finite Element Approaches on Polytopal Meshes

Steffen Weißer
Lecture Notes in Computational Science and Engineering, BEM-based Finite Element Approaches on Polytopal Meshes 130 1 (2019)
DOI: 10.1007/978-3-030-20961-2_1
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

Convergence Analysis of the mimetic Finite Difference Method for Elliptic Problems with Staggered Discretizations of Diffusion Coefficients

G. Manzini, K. Lipnikov, J. D. Moulton and M. Shashkov
SIAM Journal on Numerical Analysis 55 (6) 2956 (2017)
DOI: 10.1137/16M1108479
See this article

A Mixed Virtual Element Method for Quasi-Newtonian Stokes Flows

Ernesto Cáceres, Gabriel N. Gatica and Filánder A. Sequeira
SIAM Journal on Numerical Analysis 56 (1) 317 (2018)
DOI: 10.1137/17M1121160
See this article

Dual Virtual Element Method for Discrete Fractures Networks

Alessio Fumagalli and Eirik Keilegavlen
SIAM Journal on Scientific Computing 40 (1) B228 (2018)
DOI: 10.1137/16M1098231
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 virtual element method for stochastic Stokes equations

Wei Liu and Huoyuan Duan
Computers & Mathematics with Applications (2019)
DOI: 10.1016/j.camwa.2019.10.005
See this article

A divergence free weak virtual element method for the Stokes–Darcy problem on general meshes

Gang Wang, Feng Wang, Long Chen and Yinnian He
Computer Methods in Applied Mechanics and Engineering 344 998 (2019)
DOI: 10.1016/j.cma.2018.10.022
See this article

The mixed virtual element method on curved edges in two dimensions

Franco Dassi, Alessio Fumagalli, Davide Losapio, Stefano Scialò, Anna Scotti and Giuseppe Vacca
Computer Methods in Applied Mechanics and Engineering 386 114098 (2021)
DOI: 10.1016/j.cma.2021.114098
See this article

A three-dimensional Hellinger–Reissner virtual element method for linear elasticity problems

F. Dassi, C. Lovadina and M. Visinoni
Computer Methods in Applied Mechanics and Engineering 364 112910 (2020)
DOI: 10.1016/j.cma.2020.112910
See this article

A unified study of continuous and discontinuous Galerkin methods

Qingguo Hong, Fei Wang, Shuonan Wu and Jinchao Xu
Science China Mathematics 62 (1) 1 (2019)
DOI: 10.1007/s11425-017-9341-1
See this article

Mixed virtual element methods for elastodynamics with weak symmetry

Baiju Zhang, Yan Yang and Minfu Feng
Journal of Computational and Applied Mathematics 353 49 (2019)
DOI: 10.1016/j.cam.2018.12.020
See this article

An equilibrium-based stress recovery procedure for the VEM

E. Artioli, S. de Miranda, C. Lovadina and L. Patruno
International Journal for Numerical Methods in Engineering 117 (8) 885 (2019)
DOI: 10.1002/nme.5983
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

A multiscale approach with the Virtual Element Method: Towards a VE2 setting

F.L. Rivarola, M.F. Benedetto, N. Labanda and G. Etse
Finite Elements in Analysis and Design 158 1 (2019)
DOI: 10.1016/j.finel.2019.01.011
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

A mass, energy, enstrophy and vorticity conserving (MEEVC) mimetic spectral element discretization for the 2D incompressible Navier–Stokes equations

A. Palha and M. Gerritsma
Journal of Computational Physics 328 200 (2017)
DOI: 10.1016/j.jcp.2016.10.009
See this article

A C0 virtual element method for the biharmonic eigenvalue problem

Jian Meng and Liquan Mei
International Journal of Computer Mathematics 98 (9) 1821 (2021)
DOI: 10.1080/00207160.2020.1849635
See this article

A mixed discretization of elliptic problems on polyhedra using anisotropic hybrid meshes

Alexis B. Jawtuschenko and Ariel L. Lombardi
Calcolo 56 (2) (2019)
DOI: 10.1007/s10092-019-0303-x
See this article

The virtual element method for resistive magnetohydrodynamics

S. Naranjo Alvarez, V. Bokil, V. Gyrya and G. Manzini
Computer Methods in Applied Mechanics and Engineering 381 113815 (2021)
DOI: 10.1016/j.cma.2021.113815
See this article

A multiscale virtual element method for elliptic problems in heterogeneous porous media

Qiuqi Li and Lijian Jiang
Journal of Computational Physics 388 394 (2019)
DOI: 10.1016/j.jcp.2019.03.031
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 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

Parallel block preconditioners for three-dimensional virtual element discretizations of saddle-point problems

F. Dassi and S. Scacchi
Computer Methods in Applied Mechanics and Engineering 372 113424 (2020)
DOI: 10.1016/j.cma.2020.113424
See this article

Virtual Element approximation of 2D magnetostatic problems

L. Beirão da Veiga, F. Brezzi, F. Dassi, L.D. Marini and A. Russo
Computer Methods in Applied Mechanics and Engineering 327 173 (2017)
DOI: 10.1016/j.cma.2017.08.013
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

A Taylor–Hood type virtual element formulations for large incompressible strains

P. Wriggers, M.L. De Bellis and B. Hudobivnik
Computer Methods in Applied Mechanics and Engineering 385 114021 (2021)
DOI: 10.1016/j.cma.2021.114021
See this article

Virtual Element Methods for hyperbolic problems on polygonal meshes

Giuseppe Vacca
Computers & Mathematics with Applications 74 (5) 882 (2017)
DOI: 10.1016/j.camwa.2016.04.029
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

The curl–curl conforming virtual element method for the quad-curl problem

Jikun Zhao and Bei Zhang
Mathematical Models and Methods in Applied Sciences 31 (08) 1659 (2021)
DOI: 10.1142/S0218202521500354
See this article

Virtual elements for Maxwell's equations

L. Beirão da Veiga, F. Dassi, G. Manzini and L. Mascotto
Computers & Mathematics with Applications (2021)
DOI: 10.1016/j.camwa.2021.08.019
See this article

A local projection stabilization virtual element method for convection-diffusion-reaction equation

Yang Li and Minfu Feng
Applied Mathematics and Computation 411 126536 (2021)
DOI: 10.1016/j.amc.2021.126536
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

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

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

Dual Virtual Element Methods for Discrete Fracture Matrix models

Alessio Fumagalli, Eirik Keilegavlen, A. Anciaux-Sedrakian and Q. H. Tran
Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 74 41 (2019)
DOI: 10.2516/ogst/2019008
See this article

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

V. Gyrya and K. Lipnikov
Journal of Computational Physics 348 549 (2017)
DOI: 10.1016/j.jcp.2017.07.019
See this article

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)
DOI: 10.1016/j.mechrescom.2020.103494
See this article

Bricks for the mixed high-order virtual element method: Projectors and differential operators

F. Dassi and G. Vacca
Applied Numerical Mathematics 155 140 (2020)
DOI: 10.1016/j.apnum.2019.03.014
See this article

A virtual element method for the Laplacian eigenvalue problem in mixed form

Jian Meng, Yongchao Zhang and Liquan Mei
Applied Numerical Mathematics 156 1 (2020)
DOI: 10.1016/j.apnum.2020.03.026
See this article

Conforming and nonconforming virtual element methods for a Kirchhoff plate contact problem

Fei Wang and Jikun Zhao
IMA Journal of Numerical Analysis 41 (2) 1496 (2021)
DOI: 10.1093/imanum/draa005
See this article

Virtual elements for sound propagation in complex poroelastic media

Abhilash Sreekumar, Savvas P. Triantafyllou and Fabien Chevillotte
Computational Mechanics (2021)
DOI: 10.1007/s00466-021-02078-2
See this article

A Divergence Free Weak Virtual Element Method for the Stokes Problem on Polytopal Meshes

Long Chen and Feng Wang
Journal of Scientific Computing 78 (2) 864 (2019)
DOI: 10.1007/s10915-018-0796-5
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

Multivariate approximation at fake nodes

S. De Marchi, F. Marchetti, E. Perracchione and D. Poggiali
Applied Mathematics and Computation 391 125628 (2021)
DOI: 10.1016/j.amc.2020.125628
See this article

Robust Hybrid High-Order Method on Polytopal Meshes with Small Faces

Jérôme Droniou and Liam Yemm
Computational Methods in Applied Mathematics (2021)
DOI: 10.1515/cmam-2021-0018
See this article

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)
DOI: 10.1007/s00211-020-01167-3
See this article

A mathematical model for thermal single-phase flow and reactive transport in fractured porous media

Alessio Fumagalli and Anna Scotti
Journal of Computational Physics 434 110205 (2021)
DOI: 10.1016/j.jcp.2021.110205
See this article

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)
DOI: 10.1002/nme.6636
See this article

Finite Elements and Virtual Elements on Classical Meshes

Franco Brezzi and Luisa Donatella Marini
Vietnam Journal of Mathematics 49 (3) 871 (2021)
DOI: 10.1007/s10013-021-00474-y
See this article

A priori and a posterior error estimate of new weak Galerkin finite element methods for second order elliptic interface problems on polygonal meshes

Lin Mu
Journal of Computational and Applied Mathematics 362 423 (2019)
DOI: 10.1016/j.cam.2018.09.007
See this article

Some estimates of virtual element methods for fourth order problems

Qingguang Guan
Electronic Research Archive (2021)
DOI: 10.3934/era.2021074
See this article

A finite element framework for some mimetic finite difference discretizations

C. Rodrigo, F.J. Gaspar, X. Hu and L. Zikatanov
Computers & Mathematics with Applications 70 (11) 2661 (2015)
DOI: 10.1016/j.camwa.2015.07.012
See this article

The mimetic finite difference method for elliptic and parabolic problems with a staggered discretization of diffusion coefficient

Konstantin Lipnikov, Gianmarco Manzini, J. David Moulton and Mikhail Shashkov
Journal of Computational Physics 305 111 (2016)
DOI: 10.1016/j.jcp.2015.10.031
See this article

A mimetic method for polygons

J. Blair Perot and Chris Chartrand
Journal of Computational Physics 424 109853 (2021)
DOI: 10.1016/j.jcp.2020.109853
See this article

A paradigm for higher-order polygonal elements in finite elasticity using a gradient correction scheme

Heng Chi, Cameron Talischi, Oscar Lopez-Pamies and Glaucio H. Paulino
Computer Methods in Applied Mechanics and Engineering 306 216 (2016)
DOI: 10.1016/j.cma.2015.12.025
See this article

The superconvergence gradient recovery method for linear finite element method with polygons

Shengyong Ding, Guojian Shao, Yaoying Huang and Hougai Shi
International Journal for Numerical Methods in Engineering 122 (16) 4154 (2021)
DOI: 10.1002/nme.6698
See this article

Numerical analysis of locally conservative weak Galerkin dual-mixed finite element method for the time-dependent Poisson–Nernst–Planck system

Zeinab Gharibi, Mehdi Dehghan and Mostafa Abbaszadeh
Computers & Mathematics with Applications 92 88 (2021)
DOI: 10.1016/j.camwa.2021.03.008
See this article

An Oscillation-free Discontinuous Galerkin Method for Scalar Hyperbolic Conservation Laws

Jianfang Lu, Yong Liu and Chi-Wang Shu
SIAM Journal on Numerical Analysis 59 (3) 1299 (2021)
DOI: 10.1137/20M1354192
See this article

A modified nonconforming virtual element with BDM-like reconstruction for the Navier-Stokes equations

Xin Liu and Yufeng Nie
Applied Numerical Mathematics 167 375 (2021)
DOI: 10.1016/j.apnum.2021.05.014
See this article

A projection-based stabilized virtual element method for the unsteady incompressible Brinkman equations

Xi Zhang and Minfu Feng
Applied Mathematics and Computation 408 126325 (2021)
DOI: 10.1016/j.amc.2021.126325
See this article

Further developments on boundary-field equation methods for nonlinear transmission problems

Gabriel N. Gatica, George C. Hsiao and Salim Meddahi
Journal of Mathematical Analysis and Applications 502 (2) 125262 (2021)
DOI: 10.1016/j.jmaa.2021.125262
See this article

Polyhedral Methods in Geosciences

Alessio Fumagalli, Anna Scotti and Luca Formaggia
SEMA SIMAI Springer Series, Polyhedral Methods in Geosciences 27 299 (2021)
DOI: 10.1007/978-3-030-69363-3_8
See this article

Polyhedral Methods in Geosciences

Dibyendu Adak, Gianmarco Manzini and Sundararajan Natarajan
SEMA SIMAI Springer Series, Polyhedral Methods in Geosciences 27 259 (2021)
DOI: 10.1007/978-3-030-69363-3_7
See this article