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On mesh refinement procedures for polygonal virtual elements
Daniel van Huyssteen, Felipe Lopez Rivarola, Guillermo Etse and Paul Steinmann Applications in Engineering Science 22 100222 (2025) https://doi.org/10.1016/j.apples.2025.100222
Lowest order stabilization free virtual element method for the 2D Poisson equation
Quasi-optimal mesh generation for the virtual element method: A fully adaptive remeshing procedure
Daniel van Huyssteen, Felipe Lopez Rivarola, Guillermo Etse and Paul Steinmann Computer Methods in Applied Mechanics and Engineering 435 117630 (2025) https://doi.org/10.1016/j.cma.2024.117630
VEM approximation for the Stokes eigenvalue problem: A priori and a posteriori error analysis
A $$C^1$$-Conforming Arbitrary-Order Two-Dimensional Virtual Element Method for the Fourth-Order Phase-Field Equation
Dibyendu Adak, Gianmarco Manzini, Hashem M. Mourad, JeeYeon N. Plohr and Lampros Svolos Journal of Scientific Computing 98(2) (2024) https://doi.org/10.1007/s10915-023-02409-w
Adaptive VEM for variable data: convergence and optimality
L Beirão da Veiga, C Canuto, R H Nochetto, G Vacca and M Verani IMA Journal of Numerical Analysis 44(5) 2553 (2024) https://doi.org/10.1093/imanum/drad085
On adaptive mesh coarsening procedures for the virtual element method for two-dimensional elastic problems
Daniel van Huyssteen, Felipe Lopez Rivarola, Guillermo Etse and Paul Steinmann Computer Methods in Applied Mechanics and Engineering 418 116507 (2024) https://doi.org/10.1016/j.cma.2023.116507
Residual-based a posteriori error estimation for mixed virtual element methods
Adaptive VEM: Stabilization-Free A Posteriori Error Analysis and Contraction Property
L. Beirão da Veiga, C. Canuto, R. H. Nochetto, G. Vacca and M. Verani SIAM Journal on Numerical Analysis 61(2) 457 (2023) https://doi.org/10.1137/21M1458740
A first-order stabilization-free Virtual Element Method
Sebastian Naranjo Alvarez, Vrushali A. Bokil, Vitaliy Gyrya and Gianmarco Manzini SEMA SIMAI Springer Series, The Virtual Element Method and its Applications 31 499 (2022) https://doi.org/10.1007/978-3-030-95319-5_12
The Virtual Element Method and its Applications
Dibyendu Adak, M. Arrutselvi, E. Natarajan and S. Natarajan SEMA SIMAI Springer Series, The Virtual Element Method and its Applications 31 59 (2022) https://doi.org/10.1007/978-3-030-95319-5_2
The role of mesh quality and mesh quality indicators in the virtual element method
$ C^1 $-VEM for some variants of the Cahn-Hilliard equation: A numerical exploration
Paola F. Antonietti, Simone Scacchi, Giuseppe Vacca and Marco Verani Discrete and Continuous Dynamical Systems - S 15(8) 1919 (2022) https://doi.org/10.3934/dcdss.2022038
A priori and a posteriori error analysis of the lowest-order NCVEM for second-order linear indefinite elliptic problems
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
The Virtual Element Method and its Applications
Tommaso Sorgente, Daniele Prada, Daniela Cabiddu, et al. SEMA SIMAI Springer Series, The Virtual Element Method and its Applications 31 1 (2022) https://doi.org/10.1007/978-3-030-95319-5_1
The Virtual Element Method and its Applications
Paola F. Antonietti, Gianmarco Manzini, Ilario Mazzieri, Simone Scacchi and Marco Verani SEMA SIMAI Springer Series, The Virtual Element Method and its Applications 31 411 (2022) https://doi.org/10.1007/978-3-030-95319-5_10
On mesh refinement procedures for the virtual element method for two-dimensional elastic problems
Daniel van Huyssteen, Felipe Lopez Rivarola, Guillermo Etse and Paul Steinmann Computer Methods in Applied Mechanics and Engineering 393 114849 (2022) https://doi.org/10.1016/j.cma.2022.114849
Virtual element method for the Helmholtz transmission eigenvalue problem of anisotropic media
Dibyendu Adak, Gianmarco Manzini and Sundararajan Natarajan SEMA SIMAI Springer Series, Polyhedral Methods in Geosciences 27 259 (2021) https://doi.org/10.1007/978-3-030-69363-3_7
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) https://doi.org/10.1002/nme.6636
Error estimation for the polygonal finite element method for smooth and singular linear elasticity
Octavio A. González-Estrada, Sundararajan Natarajan, Juan José Ródenas and Stéphane P.A. Bordas Computers & Mathematics with Applications 92 109 (2021) https://doi.org/10.1016/j.camwa.2021.03.017
Arbitrary-order intrinsic virtual element method for elliptic equations on surfaces
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) https://doi.org/10.1142/S0218202521500627
Adaptive non-hierarchical Galerkin methods for parabolic problems with application to moving mesh and virtual element methods
Andrea Cangiani, Emmanuil H. Georgoulis and Oliver J. Sutton Mathematical Models and Methods in Applied Sciences 31(04) 711 (2021) https://doi.org/10.1142/S0218202521500172
A posteriori error estimate for discontinuous Galerkin finite element method on polytopal mesh
Jintao Cui, Fuzheng Gao, Zhengjia Sun and Peng Zhu Numerical Methods for Partial Differential Equations 36(3) 601 (2020) https://doi.org/10.1002/num.22443
A New Hybrid Staggered Discontinuous Galerkin Method on General Meshes
Error estimation and mesh adaptivity for the virtual element method based on recovery by compatibility in patches
Antonio Maria D'Altri, Stefano de Miranda, Luca Patruno, Edoardo Artioli and Carlo Lovadina International Journal for Numerical Methods in Engineering 121(19) 4374 (2020) https://doi.org/10.1002/nme.6438
A priori and a posteriori error estimates for a virtual element spectral analysis for the elasticity equations
A virtual element method for a nonlocal FitzHugh–Nagumo model of cardiac electrophysiology
Mauricio Sepúlveda, David Mora, Mostafa Bendahmane and Verónica Anaya IMA Journal of Numerical Analysis 40(2) 1544 (2020) https://doi.org/10.1093/imanum/drz001
Virtual element method for a nonlocal elliptic problem of Kirchhoff type on polygonal meshes
A simple and effective gradient recovery scheme and a posteriori error estimator for the Virtual Element Method (VEM)
Heng Chi, Lourenço Beirão da Veiga and Glaucio H. Paulino Computer Methods in Applied Mechanics and Engineering 347 21 (2019) https://doi.org/10.1016/j.cma.2018.08.014
Anisotropic polygonal and polyhedral discretizations in finite element analysis
Numerical Mathematics and Advanced Applications ENUMATH 2017
Paola F. Antonietti, Stefano Berrone, Marco Verani and Steffen Weißer Lecture Notes in Computational Science and Engineering, Numerical Mathematics and Advanced Applications ENUMATH 2017 126 725 (2019) https://doi.org/10.1007/978-3-319-96415-7_67
The Dual-Weighted Residual Estimator Realized on Polygonal Meshes