A multigrid algorithm for the p-version of the virtual element method
ESAIM: M2AN, 52 1 (2018) 337-364
Published online: 2018-05-28
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
(2026)
https://doi.org/10.2139/ssrn.6631877
Deep learning accelerated algebraic multigrid methods for polytopal discretizations of second-order differential problems
Paola F. Antonietti, Matteo Caldana, Lorenzo Bruno Donato Gentile and Marco VeraniMathematical Models and Methods in Applied Sciences 36 (08) 1649 (2026)
https://doi.org/10.1142/S0218202526420029
Nodal auxiliary space preconditioners for mixed virtual element methods
Wietse M. Boon and Erik NilssonESAIM: Mathematical Modelling and Numerical Analysis 59 (1) 363 (2025)
https://doi.org/10.1051/m2an/2024081
hp-Robust multigrid solver on locally refined meshes for FEM discretizations of symmetric elliptic PDEs
Michael Innerberger, Ani Miraçi, Dirk Praetorius and Julian StreitbergerESAIM: Mathematical Modelling and Numerical Analysis 58 (1) 247 (2024)
https://doi.org/10.1051/m2an/2023104
Reduced basis stabilization and post-processing for the virtual element method
Fabio Credali, Silvia Bertoluzza and Daniele PradaComputer Methods in Applied Mechanics and Engineering 420 116693 (2024)
https://doi.org/10.1016/j.cma.2023.116693
A deep learning algorithm to accelerate algebraic multigrid methods in finite element solvers of 3D elliptic PDEs
Matteo Caldana, Paola F. Antonietti and Luca Dede'Computers & Mathematics with Applications 167 217 (2024)
https://doi.org/10.1016/j.camwa.2024.05.013
A mixed virtual element method for the two-dimensional Navier-Stokes equations in stream-function formulation
Xi Zhang and Minfu FengComputers & Mathematics with Applications 175 119 (2024)
https://doi.org/10.1016/j.camwa.2024.09.020
BDDC Preconditioners for Virtual Element Approximations of the Three-Dimensional Stokes Equations
Tommaso Bevilacqua, Franco Dassi, Stefano Zampini and Simone ScacchiSIAM Journal on Scientific Computing 46 (1) A156 (2024)
https://doi.org/10.1137/23M1567679
A stabilization-free Virtual Element Method based on divergence-free projections
Stefano Berrone, Andrea Borio and Francesca MarconComputer Methods in Applied Mechanics and Engineering 424 116885 (2024)
https://doi.org/10.1016/j.cma.2024.116885
Agglomeration-Based Geometric Multigrid Schemes for the Virtual Element Method
Paola F. Antonietti, Stefano Berrone, Martina Busetto and Marco VeraniSIAM Journal on Numerical Analysis 61 (1) 223 (2023)
https://doi.org/10.1137/21M1466864
Parallel block preconditioners for virtual element discretizations of the time-dependent Maxwell equations
Nicolás A. Barnafi, Franco Dassi and Simone ScacchiJournal of Computational Physics 478 111970 (2023)
https://doi.org/10.1016/j.jcp.2023.111970
137 3 (2023)
https://doi.org/10.1007/978-3-031-20432-6_1
The role of stabilization in the virtual element method: A survey
Lorenzo MascottoComputers & Mathematics with Applications 151 244 (2023)
https://doi.org/10.1016/j.camwa.2023.09.045
Robust and scalable adaptive BDDC preconditioners for virtual element discretizations of elliptic partial differential equations in mixed form
Franco Dassi, Stefano Zampini and S. ScacchiComputer Methods in Applied Mechanics and Engineering 391 114620 (2022)
https://doi.org/10.1016/j.cma.2022.114620
Adaptive virtual element methods with equilibrated fluxes
F. Dassi, J. Gedicke and L. MascottoApplied Numerical Mathematics 173 249 (2022)
https://doi.org/10.1016/j.apnum.2021.11.015
Stabilization of the nonconforming virtual element method
S. Bertoluzza, G. Manzini, M. Pennacchio and D. PradaComputers & Mathematics with Applications 116 25 (2022)
https://doi.org/10.1016/j.camwa.2021.10.009
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
An improved multigrid solver for the p-hierarchical basis finite element method using a space decomposition smoother
Janitha GunatilakeComputers & Mathematics with Applications 124 52 (2022)
https://doi.org/10.1016/j.camwa.2022.08.019
BDDC Preconditioners for Divergence Free Virtual Element Discretizations of the Stokes Equations
Tommaso Bevilacqua and Simone ScacchiJournal of Scientific Computing 92 (2) (2022)
https://doi.org/10.1007/s10915-022-01929-1
Weakly imposed Dirichlet boundary conditions for 2D and 3D Virtual Elements
Silvia Bertoluzza, Micol Pennacchio and Daniele PradaComputer Methods in Applied Mechanics and Engineering 400 115454 (2022)
https://doi.org/10.1016/j.cma.2022.115454
A review on arbitrarily regular conforming virtual element methods for second- and higher-order elliptic partial differential equations
Paola F. Antonietti, Gianmarco Manzini, Simone Scacchi and Marco VeraniMathematical Models and Methods in Applied Sciences 31 (14) 2825 (2021)
https://doi.org/10.1142/S0218202521500627
Parallel solvers for virtual element discretizations of elliptic equations in mixed form
F. Dassi and S. ScacchiComputers & Mathematics with Applications 79 (7) 1972 (2020)
https://doi.org/10.1016/j.camwa.2019.07.027
FETI-DP for the Three Dimensional Virtual Element Method
Silvia Bertoluzza, Micol Pennacchio and Daniele PradaSIAM Journal on Numerical Analysis 58 (3) 1556 (2020)
https://doi.org/10.1137/18M1233303
A fully discrete virtual element scheme for the Cahn–Hilliard equation in mixed form
Xin Liu, Zhengkang He and Zhangxin ChenComputer Physics Communications 246 106870 (2020)
https://doi.org/10.1016/j.cpc.2019.106870
Parallel block preconditioners for three-dimensional virtual element discretizations of saddle-point problems
F. Dassi and S. ScacchiComputer Methods in Applied Mechanics and Engineering 372 113424 (2020)
https://doi.org/10.1016/j.cma.2020.113424
A numerical study of the virtual element method in anisotropic diffusion problems
Annamaria MazziaMathematics and Computers in Simulation 177 63 (2020)
https://doi.org/10.1016/j.matcom.2020.04.006
The conforming virtual element method for polyharmonic problems
P.F. Antonietti, G. Manzini and M. VeraniComputers & Mathematics with Applications 79 (7) 2021 (2020)
https://doi.org/10.1016/j.camwa.2019.09.022
The harmonic virtual element method: stabilization and exponential convergence for the Laplace problem on polygonal domains
Alexey Chernov and Lorenzo MascottoIMA Journal of Numerical Analysis 39 (4) 1787 (2019)
https://doi.org/10.1093/imanum/dry038
A posteriori error estimation and adaptivity in hp virtual elements
L. Beirão da Veiga, G. Manzini and L. MascottoNumerische Mathematik 143 (1) 139 (2019)
https://doi.org/10.1007/s00211-019-01054-6
The Virtual Element Method with curved edges
L. Beirão da Veiga, A. Russo and G. VaccaESAIM: Mathematical Modelling and Numerical Analysis 53 (2) 375 (2019)
https://doi.org/10.1051/m2an/2018052
Numerical Mathematics and Advanced Applications ENUMATH 2017
Paola F. Antonietti, Stefano Berrone, Marco Verani and Steffen WeißerLecture Notes in Computational Science and Engineering, Numerical Mathematics and Advanced Applications ENUMATH 2017 126 725 (2019)
https://doi.org/10.1007/978-3-319-96415-7_67
Non-conforming Harmonic Virtual Element Method: $$h$$ h - and $$p$$ p -Versions
Lorenzo Mascotto, Ilaria Perugia and Alexander PichlerJournal of Scientific Computing 77 (3) 1874 (2018)
https://doi.org/10.1007/s10915-018-0797-4