http://www.cnr.it/ontology/cnr/individuo/prodotto/ID211240

Basic principles of Virtual Element Methods (Articolo in rivista)

Type

Prodotto della ricerca (Classe)
Articolo in rivista (Classe)

Label

Basic principles of Virtual Element Methods (Articolo in rivista) (literal)

Anno

2013-01-01T00:00:00+01:00 (literal)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi

10.1142/S0218202512500492 (literal)

Alternative label

L. Beirão da Veiga; F. Brezzi; C. Cangiani; G. Manzini; L. D. Marini; A. Russo (2013)
Basic principles of Virtual Element Methods
in Mathematical models and methods in applied sciences; World Scientific, Singapore (Singapore)
(literal)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori

L. Beirão da Veiga; F. Brezzi; C. Cangiani; G. Manzini; L. D. Marini; A. Russo (literal)

Pagina inizio

199 (literal)

Pagina fine

214 (literal)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url

http://www.worldscientific.com/doi/abs/10.1142/S0218202512500492?journalCode=m3as (literal)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume

23 (literal)

Rivista

Mathematical models and methods in applied sciences (Rivista)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo

1 (literal)

Note

ISI Web of Science (WOS) (literal)
Scopu (literal)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni

Dipartimento di Matematica, Università di Milano Statale, via Saldini 50, I-20133 Milano, Italy; IUSS-Pavia and IMATI-CNR, via Ferrata 5a, 27100 Pavia, Italy; Department of Mathematics, King Abdulaziz University, P O Box 80203, Jeddah 21589, Saudi Arabia; Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, UK; IMATI-CNR and IUSS-Pavia, via Ferrata 5a, 27100 Pavia, Italy; Dipartimento di Matematica, Università di Pavia and IMATI-CNR, via Ferrata 1, 27100 Pavia, Italy; Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, via Cozzi 53, I-20153 Milano, Italy (literal)

Titolo

Basic principles of Virtual Element Methods (literal)

Abstract

We present, on the simplest possible case, what we consider as the very basic features of the (brand new) virtual element method. As the readers will easily recognize, the virtual element method could easily be regarded as the ultimate evolution of the mimetic finite differences approach. However, in their last step they became so close to the traditional finite elements that we decided to use a different perspective and a different name. Now the virtual element spaces are just like the usual finite element spaces with the addition of suitable non-polynomial functions. This is far from being a new idea. See for instance the very early approach of E. Wachspress [A Rational Finite Element Basic (Academic Press, 1975)] or the more recent overview of T.-P. Fries and T. Belytschko [The extended/generalized finite element method: An overview of the method and its applications, Int. J. Numer. Methods Engrg. 84 (2010) 253-304]. The novelty here is to take the spaces and the degrees of freedom in such a way that the elementary stiffness matrix can be computed without actually computing these non-polynomial functions, but just using the degrees of freedom. In doing that we can easily deal with complicated element geometries and/or higher-order continuity conditions (like C-1, C-2, etc.). The idea is quite general, and could be applied to a number of different situations and problems. Here however we want to be as clear as possible, and to present the simplest possible case that still gives the flavor of the whole idea. (literal)

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