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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
Two robust virtual element methods for the Brinkman equations
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
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) https://doi.org/10.1002/nme.6698
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
A C0 virtual element method for the biharmonic eigenvalue problem
Comparison of the response to geometrical complexity of methods for unstationary simulations in discrete fracture networks with conforming, polygonal, and non-matching grids
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
Numerical analysis of locally conservative weak Galerkin dual-mixed finite element method for the time-dependent Poisson–Nernst–Planck system
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) https://doi.org/10.1016/j.cma.2020.113251
A posteriori error analysis of a mixed virtual element method for a nonlinear Brinkman model of porous media flow
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) https://doi.org/10.1002/nme.6287
Efficient multi-material continuum topology optimization considering hyperelasticity: Achieving local feature control through regional constraints
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
Parallel solvers for virtual element discretizations of elliptic equations in mixed form
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) https://doi.org/10.1051/m2an/2020011
Parallel block preconditioners for three-dimensional virtual element discretizations of saddle-point problems
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) https://doi.org/10.2516/ogst/2019008
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) https://doi.org/10.1137/18M1200762
A priori and a posterior error estimate of new weak Galerkin finite element methods for second order elliptic interface problems on polygonal meshes
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) https://doi.org/10.1007/978-3-030-20961-2_6
Anisotropic Error Estimates of the Linear Nonconforming Virtual Element Methods
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) https://doi.org/10.1002/nme.5983
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) https://doi.org/10.1007/978-3-030-20961-2_1
A unified study of continuous and discontinuous Galerkin methods
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) https://doi.org/10.1051/m2an/2018007
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) https://doi.org/10.1137/18M1169886
Dual virtual element method in presence of an inclusion
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) https://doi.org/10.1142/S0218202518500598
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) https://doi.org/10.1137/17M1121160
An Advection-Robust Hybrid High-Order Method for the Oseen Problem
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) https://doi.org/10.1016/j.cma.2017.08.013
Flow simulations in porous media with immersed intersecting fractures