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The virtual element method

Part of: Partial differential equations, boundary value problems

Published online by Cambridge University Press:  11 May 2023

Lourenço Beirão Da Veiga ,
Franco Brezzi ,
L. Donatella Marini  and
Alessandro Russo Open the ORCID record for Alessandro Russo [Opens in a new window]
Lourenço Beirão Da Veiga
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Milano–Bicocca, Italy and IMATI-CNR, Pavia, Italy E-mail: lourenco.beirao@unimib.it
Franco Brezzi
Affiliation:
IUSS, Istituto Universitario di Studi Superiori, Pavia, Italy and IMATI-CNR, Pavia, Italy E-mail: brezzi@imati.cnr.it
L. Donatella Marini
Affiliation:
Dipartimento di Matematica, Università di Pavia, Italy, and IMATI-CNR, Pavia, Italy E-mail: marini@imati.cnr.it
Alessandro Russo
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Milano–Bicocca, Italy and IMATI-CNR, Pavia, Italy E-mail: alessandro.russo@unimib.it
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Abstract

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The present review paper has several objectives. Its primary aim is to give an idea of the general features of virtual element methods (VEMs), which were introduced about a decade ago in the field of numerical methods for partial differential equations, in order to allow decompositions of the computational domain into polygons or polyhedra of a very general shape.

Nonetheless, the paper is also addressed to readers who have already heard (and possibly read) about VEMs and are interested in gaining more precise information, in particular concerning their application in specific subfields such as ${C}^1$ -approximations of plate bending problems or approximations to problems in solid and fluid mechanics.

MSC classification

Primary: 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Acta Numerica , Volume 32 , May 2023 , pp. 123 - 202
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2023. Published by Cambridge University Press

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