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A Mixed Virtual Element Method for the Four‐Field Poroelasticity Problem on Polygonal Meshes and Its Simulation in Brain Edema
Gang Wang, Mingchao Cai, Xiaojing Dong and Yinnian He Numerical Methods for Partial Differential Equations 41(6) (2025) https://doi.org/10.1002/num.70052
A fully-discrete mixed virtual element scheme for the unsteady Navier–Stokes equation coupled with a heat transfer equation under mixed boundary conditions
Virtual element approximations of the time-fractional nonlinear convection-diffusion equation on polygonal meshes
Zaffar Mehdi Dar, M. Arrutselvi, Chandru Muthusamy, Sundararajan Natarajan and Gianmarco Manzini Mathematics in Engineering 7(2) 96 (2025) https://doi.org/10.3934/mine.2025005
A noncoforming virtual element approximation for the Oseen eigenvalue problem
Yi Yang, Jian Meng, Wei‐Long Fan, Jun Lv and Bing‐Bing Xu International Journal for Numerical Methods in Engineering 126(22) (2025) https://doi.org/10.1002/nme.70191
The virtual element method on polygonal pixel–based tessellations
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
Mixed Virtual Element approximation of linear acoustic wave equation
An enriched virtual element method for 2D‐3C generalized membrane shell model on surface
Qian Yang, Xiaoqin Shen, Jikun Zhao and Yumin Cheng International Journal for Numerical Methods in Engineering 125(8) (2024) https://doi.org/10.1002/nme.7432
A Banach spaces-based fully mixed virtual element method for the stationary two-dimensional Boussinesq equations
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
Convergence analysis of expanded mixed virtual element methods for nonlocal problems
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
Hybrid high-order methods for flow simulations in extremely large discrete fracture networks
Alexandre Ern, Florent Hédin, Géraldine Pichot and Nicolas Pignet The SMAI Journal of computational mathematics 8 375 (2023) https://doi.org/10.5802/smai-jcm.92
Virtual element method for linear elastic clamped plate model
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 virtual element method for the time fractional convection diffusion reaction equation with non-smooth data
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
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A formal construction of a divergence-free basis in the nonconforming virtual element method for the Stokes problem
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
A mixed virtual element method for the time-fractional fourth-order subdiffusion 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
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
Machine learning based refinement strategies for polyhedral grids with applications to virtual element and polyhedral discontinuous Galerkin methods
The mixed virtual element method on curved edges in two dimensions
Franco Dassi, Alessio Fumagalli, Davide Losapio, Stefano Scialò, Anna Scotti and Giuseppe Vacca Computer Methods in Applied Mechanics and Engineering 386 114098 (2021) https://doi.org/10.1016/j.cma.2021.114098
Comparison of the response to geometrical complexity of methods for unstationary simulations in discrete fracture networks with conforming, polygonal, and non-matching grids
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
A C0 virtual element method for the biharmonic eigenvalue problem
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
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
General polytopal H(div)-conformal finite elements and their discretisation spaces
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