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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 High-Order Dual Robust Virtual Element Method for the Inductionless Magnetohydrodynamic Equations
A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains
On the Coupling of the Curved Virtual Element Method with the One-Equation Boundary Element Method for 2D Exterior Helmholtz Problems
Luca Desiderio, Silvia Falletta, Matteo Ferrari and Letizia Scuderi SIAM Journal on Numerical Analysis 60(4) 2099 (2022) https://doi.org/10.1137/21M1460776
VEMPIC
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
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
The Virtual Element Method and its Applications
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
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 local projection stabilization virtual element method for convection-diffusion-reaction equation
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
Analysis of the decoupled and positivity-preserving DDFV schemes for diffusion problems 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
A Q1-finite volume element scheme for anisotropic diffusion problems on general convex quadrilateral mesh
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 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 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
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
Virtual Element Method for an Elliptic Hemivariational Inequality with Applications to Contact Mechanics
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
An Arbitrary-Order Discontinuous Galerkin Method with One Unknown Per Element
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
Virtual element formulation for isotropic damage
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
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
A residual a posteriori error estimate for the Virtual Element Method
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
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
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