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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) https://doi.org/10.1007/s10915-021-01683-w
Pressure-independent velocity error estimates for (Navier-)Stokes nonconforming virtual element discretization with divergence free
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 divergence-free weak virtual element method for the Navier-Stokes equation on polygonal meshes
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) https://doi.org/10.1002/nme.6569
A polygonal discontinuous Galerkin method with minus one stabilization
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) https://doi.org/10.1002/nme.6803
Enrichment of the nonconforming virtual element method with singular functions
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
Gradient discretization of two-phase flows coupled with mechanical deformation in fractured porous media
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
A local projection stabilization virtual element method for convection-diffusion-reaction equation
Virtual element methods for the spatial discretisation of the multigroup neutron diffusion equation on polygonal meshes with applications to nuclear reactor physics
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 divergence-free reconstruction of the nonconforming virtual element method for the Stokes problem
An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids
Paola Antonietti, Paul Houston, Giorgio Pennesi and Endre Süli Mathematics of Computation 89(325) 2047 (2020) https://doi.org/10.1090/mcom/3510
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 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) https://doi.org/10.1137/19M1286499
The nonconforming virtual element method for fourth-order singular perturbation problem
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) https://doi.org/10.1002/num.22439
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
Virtual element methods for nonlocal parabolic problems on general type of meshes
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) https://doi.org/10.1142/S0218202520500311
The p- and hp-versions of the virtual element method for elliptic eigenvalue problems
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) https://doi.org/10.1002/nme.6137
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) https://doi.org/10.1002/num.22298
A virtual element method for the coupled Stokes–Darcy problem with the Beaver–Joseph–Saffman interface condition
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) https://doi.org/10.1142/S0218202519500301
n-sided polygonal hybrid finite elements with unified fundamental solution kernels for topology optimization