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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
Unconditional error analysis of linearized BDF2 mixed virtual element method for semilinear parabolic problems on polygonal meshes
Stabilization‐free virtual element method for 2D elastoplastic problems
Bing‐Bing Xu, Yi‐Fan Wang and Peter Wriggers International Journal for Numerical Methods in Engineering 125(15) (2024) https://doi.org/10.1002/nme.7490
The virtual element method on polygonal pixel–based tessellations
A posteriori error estimates for hierarchical mixed-dimensional elliptic equations
Jhabriel Varela, Elyes Ahmed, Eirik Keilegavlen, Jan M. Nordbotten and Florin A. Radu Journal of Numerical Mathematics 31(4) 247 (2023) https://doi.org/10.1515/jnma-2022-0038
The nonconforming locking-free virtual element method for the Biot's consolidation model in poroelasticity
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
The virtual element method for a 2D incompressible MHD system
S. Naranjo-Alvarez, L. Beirão da Veiga, V.A. Bokil, F. Dassi, V. Gyrya and G. Manzini Mathematics and Computers in Simulation 211 301 (2023) https://doi.org/10.1016/j.matcom.2023.03.029
The mixed virtual element discretization for highly-anisotropic problems: the role of the boundary degrees of freedom
Resolving vibro‐acoustics in poroelastic media via a multiscale virtual element method
Abhilash Sreekumar, Savvas P. Triantafyllou, Fabien Chevillotte and François‐Xavier Bécot International Journal for Numerical Methods in Engineering 124(7) 1510 (2023) https://doi.org/10.1002/nme.7173
Unconditionally energy stable C0-virtual element scheme for solving generalized Swift-Hohenberg equation
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
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
Robust and scalable adaptive BDDC preconditioners for virtual element discretizations of elliptic partial differential equations in mixed form
An arbitrary order Mixed Virtual Element formulation for coupled multi-dimensional flow problems
M.F. Benedetto, A. Borio, F. Kyburg, J. Mollica and S. Scialò Computer Methods in Applied Mechanics and Engineering 391 114204 (2022) https://doi.org/10.1016/j.cma.2021.114204
The Virtual Element Method and its Applications
Daniele Boffi, Francesca Gardini and Lucia Gastaldi SEMA SIMAI Springer Series, The Virtual Element Method and its Applications 31 275 (2022) https://doi.org/10.1007/978-3-030-95319-5_7
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
A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem
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
Refinement of polygonal grids using Convolutional Neural Networks with applications to polygonal Discontinuous Galerkin and Virtual Element methods
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) https://doi.org/10.1051/m2an/2021050
An Lp spaces-based mixed virtual element method for the two-dimensional Navier–Stokes equations
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
A robust VEM-based approach for flow simulations in poro-fractured media
Stefano Berrone, Andrea Borio, Alessandro D’Auria, Stefano Scialò and Fabio Vicini Mathematical Models and Methods in Applied Sciences 31(14) 2855 (2021) https://doi.org/10.1142/S0218202521500639
A divergence-free weak virtual element method for the Navier-Stokes equation on polygonal meshes
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
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) https://doi.org/10.1016/j.cma.2021.113815
A priori error analysis for a mixed VEM discretization of the spectral problem for the Laplacian operator
Comparison of the response to geometrical complexity of methods for unstationary simulations in discrete fracture networks with conforming, polygonal, and non-matching grids
Virtual element methods for the spatial discretisation of the multigroup neutron diffusion equation on polygonal meshes with applications to nuclear reactor physics
J. L. Gracia and D. Irisarri Springer Proceedings in Mathematics & Statistics, Differential Equations and Applications 368 1 (2021) https://doi.org/10.1007/978-981-16-7546-1_1
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) https://doi.org/10.1051/m2an/2020064
General polytopal H(div)-conformal finite elements and their discretisation spaces
Rémi Abgrall, Élise Le Mélédo and Philipp Öffner ESAIM: Mathematical Modelling and Numerical Analysis 55 S677 (2021) https://doi.org/10.1051/m2an/2020048
Parallel solvers for virtual element discretizations of elliptic equations in mixed form
FETI-DP for the Three Dimensional Virtual Element Method
Silvia Bertoluzza, Micol Pennacchio and Daniele Prada SIAM Journal on Numerical Analysis 58(3) 1556 (2020) https://doi.org/10.1137/18M1233303
Sharp algebraic and total a posteriori error bounds for h and p finite elements via a multilevel approach. Recovering mass balance in any situation
Jan Papež, Ulrich Rüde, Martin Vohralík and Barbara Wohlmuth Computer Methods in Applied Mechanics and Engineering 371 113243 (2020) https://doi.org/10.1016/j.cma.2020.113243