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Virtual element approximations of the time-fractional nonlinear convection-diffusion equation on polygonal meshes
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A monotone finite volume scheme for single phase flow with reactive transport in anisotropic porous media
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On stabilized equal-order virtual element methods for the Navier-Stokes equations on polygonal meshes
Edoardo Artioli, Stefano de Miranda, Carlo Lovadina, Luca Patruno and Michele Visinoni SEMA SIMAI Springer Series, The Virtual Element Method and its Applications 31 137 (2022) https://doi.org/10.1007/978-3-030-95319-5_4
A posteriori error estimation for a C1 virtual element method of Kirchhoff plates
A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains
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
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
The Virtual Element Method and its Applications
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
Tommaso Sorgente, Daniele Prada, Daniela Cabiddu, et al. SEMA SIMAI Springer Series, The Virtual Element Method and its Applications 31 1 (2022) https://doi.org/10.1007/978-3-030-95319-5_1
The Virtual Element Method and its Applications
Peter Wriggers, Fadi Aldakheel and Blaž Hudobivnik SEMA SIMAI Springer Series, The Virtual Element Method and its Applications 31 557 (2022) https://doi.org/10.1007/978-3-030-95319-5_13
Optimal Maximum Norm Estimates for Virtual Element Methods
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 Novel Cell-Centered Approach of Upwind Types for Convection Diffusion Equations on General 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
A Q1-finite volume element scheme for anisotropic diffusion problems on general convex quadrilateral mesh
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 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
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 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 least squares method for linear elasticity using a patch reconstructed space
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
A finite element method by patch reconstruction for the Stokes problem using mixed formulations
A computational framework for brittle crack-propagation based on efficient virtual element method
Ali Hussein, Fadi Aldakheel, Blaž Hudobivnik, Peter Wriggers, Pierre-Alain Guidault and Olivier Allix Finite Elements in Analysis and Design 159 15 (2019) https://doi.org/10.1016/j.finel.2019.03.001
Virtual Element Method for an Elliptic Hemivariational Inequality with Applications to Contact Mechanics
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
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
SUPG stabilization for the nonconforming virtual element method for advection–diffusion–reaction equations
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
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
Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshes
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
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 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
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
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
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