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Virtual element approximations of the time-fractional nonlinear convection-diffusion equation on polygonal meshes
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A High-Order Dual Robust Virtual Element Method for the Inductionless Magnetohydrodynamic Equations
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A discontinuous Galerkin method for a coupled Stokes–Biot problem
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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The Virtual Element Method and its Applications
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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
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
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
Stabilization of the nonconforming virtual element method
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
Multigrid solvers for multipoint flux approximations of the Darcy problem on rough quadrilateral grids
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
An implementation of mimetic finite difference method for fractured reservoirs using a fully implicit approach and discrete fracture models
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 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
Recovery-based error estimators for the VEM and BEM-based FEM
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 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
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 least squares method for linear elasticity using a patch reconstructed space
The nonconforming Virtual Element Method for eigenvalue problems
Francesca Gardini, Gianmarco Manzini and Giuseppe Vacca ESAIM: Mathematical Modelling and Numerical Analysis 53(3) 749 (2019) https://doi.org/10.1051/m2an/2018074
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
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
Anisotropic Error Estimates of the Linear Virtual Element Method on Polygonal Meshes
Unified formulation and analysis of mixed and primal discontinuous skeletal methods on polytopal meshes
Daniele Boffi and Daniele A. Di Pietro ESAIM: Mathematical Modelling and Numerical Analysis 52(1) 1 (2018) https://doi.org/10.1051/m2an/2017036
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
An enhanced octree polyhedral scaled boundary finite element method and its applications in structure analysis
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
A residual a posteriori error estimate for the Virtual Element Method
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
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
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
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
Spectral properties and conservation laws in Mimetic Finite Difference methods for PDEs