ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN)

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
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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
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Conforming and nonconforming conservative virtual element methods for nonlinear Schrödinger equation: A unified framework

Meng Li, Jikun Zhao, Nan Wang and Shaochun Chen
Computer Methods in Applied Mechanics and Engineering 380 113793 (2021)
DOI: 10.1016/j.cma.2021.113793
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Lowest-order virtual element methods for linear elasticity problems

Do Y. Kwak and Hyeokjoo Park
Computer Methods in Applied Mechanics and Engineering 390 114448 (2022)
DOI: 10.1016/j.cma.2021.114448
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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)
DOI: 10.1016/j.cam.2022.115026
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A polygonal discontinuous Galerkin method with minus one stabilization

Silvia Bertoluzza and Daniele Prada
ESAIM: Mathematical Modelling and Numerical Analysis 55 S785 (2021)
DOI: 10.1051/m2an/2020059
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Piecewise Divergence-Free Nonconforming Virtual Elements for Stokes Problem in Any Dimensions

Huayi Wei, Xuehai Huang and Ao Li
SIAM Journal on Numerical Analysis 59 (3) 1835 (2021)
DOI: 10.1137/20M1350479
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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
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The virtual element method for a nonhomogeneous double obstacle problem of Kirchhoff plate

Fang Feng and Jianguo Huang
Nonlinear Analysis: Real World Applications 71 103831 (2023)
DOI: 10.1016/j.nonrwa.2023.103831
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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
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Some Estimates for Virtual Element Methods

Susanne C. Brenner, Qingguang Guan and Li-Yeng Sung
Computational Methods in Applied Mathematics 17 (4) 553 (2017)
DOI: 10.1515/cmam-2017-0008
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The NonConforming Virtual Element Method for the Stokes Equations

Andrea Cangiani, Vitaliy Gyrya and Gianmarco Manzini
SIAM Journal on Numerical Analysis 54 (6) 3411 (2016)
DOI: 10.1137/15M1049531
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Preface

L. Beirão da Veiga and A. Ern
ESAIM: Mathematical Modelling and Numerical Analysis 50 (3) 633 (2016)
DOI: 10.1051/m2an/2016034
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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
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Conforming and nonconforming virtual element methods for elliptic problems

Andrea Cangiani, Gianmarco Manzini and Oliver J. Sutton
IMA Journal of Numerical Analysis drw036 (2016)
DOI: 10.1093/imanum/drw036
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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
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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
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Poly-Spline Finite-Element Method

Teseo Schneider, Jérémie Dumas, Xifeng Gao, et al.
ACM Transactions on Graphics 38 (3) 1 (2019)
DOI: 10.1145/3313797
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Enrichment of the nonconforming virtual element method with singular functions

E. Artioli and L. Mascotto
Computer Methods in Applied Mechanics and Engineering 385 114024 (2021)
DOI: 10.1016/j.cma.2021.114024
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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
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Finite element methods: Research in India over the last decade

Neela Nataraj and A. S. Vasudeva Murthy
Indian Journal of Pure and Applied Mathematics 50 (3) 739 (2019)
DOI: 10.1007/s13226-019-0352-5
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A Hybrid High-Order Discretization Combined with Nitsche's Method for Contact and Tresca Friction in Small Strain Elasticity

Franz Chouly, Alexandre Ern and Nicolas Pignet
SIAM Journal on Scientific Computing 42 (4) A2300 (2020)
DOI: 10.1137/19M1286499
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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
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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
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Anisotropic Error Estimates of the Linear Virtual Element Method on Polygonal Meshes

Shuhao Cao and Long Chen
SIAM Journal on Numerical Analysis 56 (5) 2913 (2018)
DOI: 10.1137/17M1154369
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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
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Ws,p-approximation properties of elliptic projectors on polynomial spaces, with application to the error analysis of a Hybrid High-Order discretisation of Leray–Lions problems

Daniele A. Di Pietro and Jérôme Droniou
Mathematical Models and Methods in Applied Sciences 27 (05) 879 (2017)
DOI: 10.1142/S0218202517500191
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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
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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
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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
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An Unfitted Hybrid High-Order Method for Elliptic Interface Problems

Erik Burman and Alexandre Ern
SIAM Journal on Numerical Analysis 56 (3) 1525 (2018)
DOI: 10.1137/17M1154266
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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
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Virtual element method for semilinear sine–Gordon equation over polygonal mesh using product approximation technique

D. Adak and S. Natarajan
Mathematics and Computers in Simulation 172 224 (2020)
DOI: 10.1016/j.matcom.2019.12.007
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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
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SUPG-stabilized virtual elements for diffusion-convection problems: a robustness analysis

Lourenco Beirão da Veiga, Franco Dassi, Carlo Lovadina and Giuseppe Vacca
ESAIM: Mathematical Modelling and Numerical Analysis 55 (5) 2233 (2021)
DOI: 10.1051/m2an/2021050
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The arbitrary‐order virtual element method for linear elastodynamics models: convergence, stability and dispersion‐dissipation analysis

Paola F. Antonietti, Gianmarco Manzini, Ilario Mazzieri, Hashem M. Mourad and Marco Verani
International Journal for Numerical Methods in Engineering 122 (4) 934 (2021)
DOI: 10.1002/nme.6569
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High-order Virtual Element Method on polyhedral meshes

L. Beirão da Veiga, F. Dassi and A. Russo
Computers & Mathematics with Applications 74 (5) 1110 (2017)
DOI: 10.1016/j.camwa.2017.03.021
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Fast Numerical Integration on Polytopic Meshes with Applications to Discontinuous Galerkin Finite Element Methods

Paola F. Antonietti, Paul Houston and Giorgio Pennesi
Journal of Scientific Computing 77 (3) 1339 (2018)
DOI: 10.1007/s10915-018-0802-y
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A nonconforming Trefftz virtual element method for the Helmholtz problem

Lorenzo Mascotto, Ilaria Perugia and Alexander Pichler
Mathematical Models and Methods in Applied Sciences 29 (09) 1619 (2019)
DOI: 10.1142/S0218202519500301
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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
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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
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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
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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
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A Hybrid High‐Order method for finite elastoplastic deformations within a logarithmic strain framework

Mickaël Abbas, Alexandre Ern and Nicolas Pignet
International Journal for Numerical Methods in Engineering 120 (3) 303 (2019)
DOI: 10.1002/nme.6137
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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)
DOI: 10.1016/j.cma.2018.05.027
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Virtual Element Method for the Laplace-Beltrami equation on surfaces

Massimo Frittelli and Ivonne Sgura
ESAIM: Mathematical Modelling and Numerical Analysis 52 (3) 965 (2018)
DOI: 10.1051/m2an/2017040
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Virtual element method for quasilinear elliptic problems

A Cangiani, P Chatzipantelidis, G Diwan and E H Georgoulis
IMA Journal of Numerical Analysis 40 (4) 2450 (2020)
DOI: 10.1093/imanum/drz035
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A quasi-optimal variant of the hybrid high-order method for elliptic partial differential equations with H−1 loads

Alexandre Ern and Pietro Zanotti
IMA Journal of Numerical Analysis 40 (4) 2163 (2020)
DOI: 10.1093/imanum/drz057
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n-sided polygonal hybrid finite elements with unified fundamental solution kernels for topology optimization

Hui Wang, Qing-Hua Qin and Cheuk-Yu Lee
Applied Mathematical Modelling 66 97 (2019)
DOI: 10.1016/j.apm.2018.09.014
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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
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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
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Non-conforming Harmonic Virtual Element Method: $$h$$h- and $$p$$p-Versions

Lorenzo Mascotto, Ilaria Perugia and Alexander Pichler
Journal of Scientific Computing 77 (3) 1874 (2018)
DOI: 10.1007/s10915-018-0797-4
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Towards robust, fast solutions of elliptic equations on complex domains through hybrid high‐order discretizations and non‐nested multigrid methods

Daniele A. Di Pietro, Frank Hülsemann, Pierre Matalon, Paul Mycek, Ulrich Rüde and Daniel Ruiz
International Journal for Numerical Methods in Engineering 122 (22) 6576 (2021)
DOI: 10.1002/nme.6803
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A Hybrid High-Order method for the incompressible Navier–Stokes equations based on Temam's device

Lorenzo Botti, Daniele A. Di Pietro and Jérôme Droniou
Journal of Computational Physics 376 786 (2019)
DOI: 10.1016/j.jcp.2018.10.014
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A high-order conservative remap for discontinuous Galerkin schemes on curvilinear polygonal meshes

Konstantin Lipnikov and Nathaniel Morgan
Journal of Computational Physics 399 108931 (2019)
DOI: 10.1016/j.jcp.2019.108931
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Gradient discretization of two-phase flows coupled with mechanical deformation in fractured porous media

Francesco Bonaldi, Konstantin Brenner, Jérôme Droniou and Roland Masson
Computers & Mathematics with Applications 98 40 (2021)
DOI: 10.1016/j.camwa.2021.06.017
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Hybrid High-Order Methods for the Acoustic Wave Equation in the Time Domain

Erik Burman, Omar Duran and Alexandre Ern
Communications on Applied Mathematics and Computation 4 (2) 597 (2022)
DOI: 10.1007/s42967-021-00131-8
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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
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A nonconforming Trefftz virtual element method for the Helmholtz problem: Numerical aspects

Lorenzo Mascotto, Ilaria Perugia and Alexander Pichler
Computer Methods in Applied Mechanics and Engineering 347 445 (2019)
DOI: 10.1016/j.cma.2018.12.039
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Serendipity Virtual Elements for General Elliptic Equations in Three Dimensions

Lourenço Beirão Da Veiga, Franco Brezzi, Franco Dassi, Luisa Donatelia Marini and Alessandro Russo
Chinese Annals of Mathematics, Series B 39 (2) 315 (2018)
DOI: 10.1007/s11401-018-1066-4
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Nonconforming virtual element method for 2mth order partial differential equations in $${\mathbb {R}}^n$$ with $$m>n$$

Xuehai Huang
Calcolo 57 (4) (2020)
DOI: 10.1007/s10092-020-00381-7
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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
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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
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The nonconforming virtual element method for parabolic problems

Jikun Zhao, Bei Zhang and Xiaopeng Zhu
Applied Numerical Mathematics 143 97 (2019)
DOI: 10.1016/j.apnum.2019.04.002
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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)
DOI: 10.1016/j.apnum.2019.04.005
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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)
DOI: 10.1016/j.cam.2020.113229
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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
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An extended P1-nonconforming finite element method on general polytopal partitions

Yujie Liu and Junping Wang
Journal of Computational and Applied Mathematics 381 113021 (2021)
DOI: 10.1016/j.cam.2020.113021
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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
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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
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The Nonconforming Virtual Element Method for a Stationary Stokes Hemivariational Inequality with Slip Boundary Condition

Min Ling, Fei Wang and Weimin Han
Journal of Scientific Computing 85 (3) (2020)
DOI: 10.1007/s10915-020-01333-7
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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
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Bridging the hybrid high-order and virtual element methods

Simon Lemaire
IMA Journal of Numerical Analysis 41 (1) 549 (2021)
DOI: 10.1093/imanum/drz056
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Hybrid high-order discretizations combined with Nitsche’s method for Dirichlet and Signorini boundary conditions

Karol L Cascavita, Franz Chouly and Alexandre Ern
IMA Journal of Numerical Analysis 40 (4) 2189 (2020)
DOI: 10.1093/imanum/drz038
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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)
DOI: 10.1016/j.aml.2021.107531
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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
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The p- and hp-versions of the virtual element method for elliptic eigenvalue problems

O. Čertík, F. Gardini, G. Manzini, L. Mascotto and G. Vacca
Computers & Mathematics with Applications 79 (7) 2035 (2020)
DOI: 10.1016/j.camwa.2019.10.018
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The nonconforming virtual element method for fourth-order singular perturbation problem

Bei Zhang, Jikun Zhao and Shaochun Chen
Advances in Computational Mathematics 46 (2) (2020)
DOI: 10.1007/s10444-020-09743-9
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A Hybrid High-Order method for incremental associative plasticity with small deformations

Mickaël Abbas, Alexandre Ern and Nicolas Pignet
Computer Methods in Applied Mechanics and Engineering 346 891 (2019)
DOI: 10.1016/j.cma.2018.08.037
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A hybrid high‐order formulation for a Neumann problem on polytopal meshes

Rommel Bustinza and Jonathan Munguia‐La‐Cotera
Numerical Methods for Partial Differential Equations 36 (3) 524 (2020)
DOI: 10.1002/num.22439
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Virtual element methods for nonlocal parabolic problems on general type of meshes

D. Adak and S. Natarajan
Advances in Computational Mathematics 46 (5) (2020)
DOI: 10.1007/s10444-020-09811-0
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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)
DOI: 10.1051/m2an/2018074
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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
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Hybrid High-Order Methods for the Elliptic Obstacle Problem

Matteo Cicuttin, Alexandre Ern and Thirupathi Gudi
Journal of Scientific Computing 83 (1) (2020)
DOI: 10.1007/s10915-020-01195-z
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Virtual elements for sound propagation in complex poroelastic media

Abhilash Sreekumar, Savvas P. Triantafyllou and Fabien Chevillotte
Computational Mechanics 69 (1) 347 (2022)
DOI: 10.1007/s00466-021-02078-2
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The Hybrid High-Order Method for Polytopal Meshes

Daniele Antonio Di Pietro and Jérôme Droniou
MS&A, The Hybrid High-Order Method for Polytopal Meshes 19 185 (2020)
DOI: 10.1007/978-3-030-37203-3_5
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Some error analysis on virtual element methods

Long Chen and Jianguo Huang
Calcolo 55 (1) (2018)
DOI: 10.1007/s10092-018-0249-4
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Discontinuous Skeletal Gradient Discretisation methods on polytopal meshes

Daniele A. Di Pietro, Jérôme Droniou and Gianmarco Manzini
Journal of Computational Physics 355 397 (2018)
DOI: 10.1016/j.jcp.2017.11.018
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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)
DOI: 10.1142/S0218202520500311
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A posteriori error estimation and adaptivity in hp virtual elements

L. Beirão da Veiga, G. Manzini and L. Mascotto
Numerische Mathematik 143 (1) 139 (2019)
DOI: 10.1007/s00211-019-01054-6
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The virtual element method for an obstacle problem of a Kirchhoff-Love plate

Fang Feng, Weimin Han and Jianguo Huang
Communications in Nonlinear Science and Numerical Simulation 103 106008 (2021)
DOI: 10.1016/j.cnsns.2021.106008
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Robust nonconforming virtual element methods for general fourth-order problems with varying coefficients

Andreas Dedner and Alice Hodson
IMA Journal of Numerical Analysis 42 (2) 1364 (2022)
DOI: 10.1093/imanum/drab003
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Conservative high-order discontinuous Galerkin remap scheme on curvilinear polyhedral meshes

Konstantin Lipnikov and Nathaniel Morgan
Journal of Computational Physics 420 109712 (2020)
DOI: 10.1016/j.jcp.2020.109712
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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
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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
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Unified analysis of discontinuous Galerkin approximations of flows in fractured porous media on polygonal and polyhedral grids

Paola F. Antonietti, Chiara Facciolà and Marco Verani
Mathematics in Engineering 2 (2) 340 (2020)
DOI: 10.3934/mine.2020017
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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
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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
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Polyhedral Methods in Geosciences

Paola F. Antonietti, Chiara Facciolà, Paul Houston, et al.
SEMA SIMAI Springer Series, Polyhedral Methods in Geosciences 27 159 (2021)
DOI: 10.1007/978-3-030-69363-3_5
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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
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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)
DOI: 10.1016/j.camwa.2017.05.016
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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
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A divergence-free weak virtual element method for the Navier-Stokes equation on polygonal meshes

Gang Wang, Feng Wang and Yinnian He
Advances in Computational Mathematics 47 (6) (2021)
DOI: 10.1007/s10444-021-09909-z
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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)
DOI: 10.1007/s10915-021-01683-w
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A theoretical and numerical analysis of a Dirichlet-Neumann domain decomposition method for diffusion problems in heterogeneous media

Alex Viguerie, Silvia Bertoluzza, Alessandro Veneziani and Ferdinando Auricchio
Applied Numerical Mathematics 173 94 (2022)
DOI: 10.1016/j.apnum.2021.11.012
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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)
DOI: 10.1007/s11075-021-01195-6
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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)
DOI: 10.1142/S0218202521500627
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Local tangential lifting virtual element method for the diffusion–reaction equation on the non-flat Voronoi discretized surface

Jingwei Li, Xinlong Feng and Yinnian He
Engineering with Computers 38 (6) 5297 (2022)
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