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A monotone finite volume scheme for single phase flow with reactive transport in anisotropic porous media
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A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains
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The Virtual Element Method and its Applications
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Virtual element approximation of two-dimensional parabolic variational inequalities
Michael Tao, Christopher Batty, Mirela Ben-Chen, Eugene Fiume and David I. W. Levin ACM Transactions on Graphics 41(4) 1 (2022) https://doi.org/10.1145/3528223.3530138
On the Coupling of the Curved Virtual Element Method with the One-Equation Boundary Element Method for 2D Exterior Helmholtz Problems
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The Virtual Element Method and its Applications
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Optimal Maximum Norm Estimates for Virtual Element Methods
The virtual element method for resistive magnetohydrodynamics
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Multiscale VEM for the Biot consolidation analysis of complex and highly heterogeneous domains
Abhilash Sreekumar, Savvas P. Triantafyllou, François-Xavier Bécot and Fabien Chevillotte Computer Methods in Applied Mechanics and Engineering 375 113543 (2021) https://doi.org/10.1016/j.cma.2020.113543
A discontinuous Galerkin method by patch reconstruction for convection-diffusion-reaction problems over polytopic meshes
A high-order discontinuous Galerkin approach to the elasto-acoustic problem
Paola F. Antonietti, Francesco Bonaldi and Ilario Mazzieri Computer Methods in Applied Mechanics and Engineering 358 112634 (2020) https://doi.org/10.1016/j.cma.2019.112634
A $ C^0P_2 $ time-stepping virtual element method for linear wave equations on polygonal meshes
A. Hussein, P. Wriggers, B. Hudobivnik, et al. Lecture Notes in Applied and Computational Mechanics, Virtual Design and Validation 93 201 (2020) https://doi.org/10.1007/978-3-030-38156-1_11
Recovery-based error estimators for the VEM and BEM-based FEM
Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra
Daniele A. Di Pietro, Jérôme Droniou and Francesca Rapetti Mathematical Models and Methods in Applied Sciences 30(09) 1809 (2020) https://doi.org/10.1142/S0218202520500372
A Q1-finite volume element scheme for anisotropic diffusion problems on general convex quadrilateral mesh
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
A discontinuous Galerkin method for Stokes equation by divergence‐free patch reconstruction
Ruo Li, Zhiyuan Sun and Zhijian Yang Numerical Methods for Partial Differential Equations 36(4) 756 (2020) https://doi.org/10.1002/num.22449
A monotone combination scheme of diffusion equations on polygonal meshes
Fei Zhao, Zhiqiang Sheng and Guangwei Yuan ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 100(5) (2020) https://doi.org/10.1002/zamm.201900320
The conforming virtual element method for polyharmonic problems
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
Solving Eigenvalue Problems in a Discontinuous Approximation Space by Patch Reconstruction
Maria Laura De Bellis, Peter Wriggers, Blaž Hudobivnik and Giorgio Zavarise Finite Elements in Analysis and Design 144 38 (2018) https://doi.org/10.1016/j.finel.2018.01.002
Phase-field modeling of brittle fracture using an efficient virtual element scheme
Fadi Aldakheel, Blaž Hudobivnik, Ali Hussein and Peter Wriggers Computer Methods in Applied Mechanics and Engineering 341 443 (2018) https://doi.org/10.1016/j.cma.2018.07.008
Anisotropic Error Estimates of the Linear Virtual Element Method on Polygonal Meshes
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
Mimetic finite difference methods for Hamiltonian wave equations in 2D
A stress/displacement Virtual Element method for plane elasticity problems
E. Artioli, S. de Miranda, C. Lovadina and L. Patruno Computer Methods in Applied Mechanics and Engineering 325 155 (2017) https://doi.org/10.1016/j.cma.2017.06.036
D. D. Filippov, I. Yu. Kudryashov, D. Yu. Maksimov, D. A. Mitrushkin, B. V. Vasekin and A. P. Roshchektaev (2017) https://doi.org/10.2118/187799-MS
Gradient schemes: Generic tools for the numerical analysis of diffusion equations
Jérome Droniou, Robert Eymard and Raphaèle Herbin ESAIM: Mathematical Modelling and Numerical Analysis 50(3) 749 (2016) https://doi.org/10.1051/m2an/2015079
Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations
Konstantin Lipnikov and Gianmarco Manzini Lecture Notes in Computational Science and Engineering, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations 114 311 (2016) https://doi.org/10.1007/978-3-319-41640-3_10
Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations
Paola F. Antonietti, Andrea Cangiani, Joe Collis, et al. Lecture Notes in Computational Science and Engineering, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations 114 281 (2016) https://doi.org/10.1007/978-3-319-41640-3_9
The nonconforming virtual element method for plate bending problems
A vertex‐centered linearity‐preserving discretization of diffusion problems on polygonal meshes
Jiming Wu, Zhiming Gao and Zihuan Dai International Journal for Numerical Methods in Fluids 81(3) 131 (2016) https://doi.org/10.1002/fld.4178
Mimetic finite difference approximation of flows in fractured porous media
Paola F. Antonietti, Luca Formaggia, Anna Scotti, Marco Verani and Nicola Verzott ESAIM: Mathematical Modelling and Numerical Analysis 50(3) 809 (2016) https://doi.org/10.1051/m2an/2015087
Spectral properties and conservation laws in Mimetic Finite Difference methods for PDEs
The arbitrary order mixed mimetic finite difference method for the diffusion equation
Vitaliy Gyrya, Konstantin Lipnikov and Gianmarco Manzini ESAIM: Mathematical Modelling and Numerical Analysis 50(3) 851 (2016) https://doi.org/10.1051/m2an/2015088
The nonconforming virtual element method
Blanca Ayuso de Dios, Konstantin Lipnikov and Gianmarco Manzini ESAIM: Mathematical Modelling and Numerical Analysis 50(3) 879 (2016) https://doi.org/10.1051/m2an/2015090
Virtual Element Method for general second-order elliptic problems on polygonal meshes
L. Beirão da Veiga, F. Brezzi, L. D. Marini and A. Russo Mathematical Models and Methods in Applied Sciences 26(04) 729 (2016) https://doi.org/10.1142/S0218202516500160
A positive scheme for diffusion problems on deformed meshes
Xavier Blanc and Emmanuel Labourasse ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 96(6) 660 (2016) https://doi.org/10.1002/zamm.201400234
Low-order reconstruction operators on polyhedral meshes: application to compatible discrete operator schemes
Post processing of solution and flux for the nodal mimetic finite difference method
Lourenço Beirão da Veiga, Gianmarco Manzini and Mario Putti Numerical Methods for Partial Differential Equations 31(1) 336 (2015) https://doi.org/10.1002/num.21907