http://www.cnr.it/ontology/cnr/individuo/prodotto/ID285916

New perspectives on polygonal and polyhedral finite element methods (Articolo in rivista)

Type

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

Label

New perspectives on polygonal and polyhedral finite element methods (Articolo in rivista) (literal)

Anno

2014-01-01T00:00:00+01:00 (literal)

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

10.1142/S0218202514400065 (literal)

Alternative label

Manzini, Gianmarco; Russo, Alessandro; Sukumar, N. (2014)
New perspectives on polygonal and polyhedral finite element methods
in Mathematical models and methods in applied sciences; World Scientific, Singapore (Singapore)
(literal)

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

Manzini, Gianmarco; Russo, Alessandro; Sukumar, N. (literal)

Pagina inizio

1665 (literal)

Pagina fine

1699 (literal)

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

http://www.worldscientific.com/doi/abs/10.1142/S0218202514400065 (literal)

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

24 (literal)

Rivista

Mathematical models and methods in applied sciences (Rivista)

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

35 (literal)

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

8 (literal)

Note

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

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

Los Alamos National Laboratory; Consiglio Nazionale delle Ricerche (CNR); University of Milano-Bicocca; University of California Davis (literal)

Titolo

New perspectives on polygonal and polyhedral finite element methods (literal)

Abstract

Generalized barycentric coordinates such as Wachspress and mean value coordinates have been used in polygonal and polyhedral finite element methods. Recently, mimetic finite difference schemes were cast within a variational framework, and a consistent and stable finite element method on arbitrary polygonal meshes was devised. The method was coined as the virtual element method (VEM), since it did not require the explicit construction of basis functions. This advance provides a more in-depth understanding of mimetic schemes, and also endows polygonal-based Galerkin methods with greater flexibility than three-node and four-node finite element methods. In the VEM, a projection operator is used to realize the decomposition of the stiffness matrix into two terms: a consistent matrix that is known, and a stability matrix that must be positive semi-definite and which is only required to scale like the consistent matrix. In this paper, we first present an overview of previous developments on conforming polygonal and polyhedral finite elements, and then appeal to the exact decomposition in the VEM to obtain a robust and efficient generalized barycentric coordinate-based Galerkin method on polygonal and polyhedral elements. The consistent matrix of the VEM is adopted, and numerical quadrature with generalized barycentric coordinates is used to compute the stability matrix. This facilitates post-processing of field variables and visualization in the VEM, and on the other hand, provides a means to exactly satisfy the patch test with efficient numerical integration in polygonal and polyhedral finite elements. We present numerical examples that demonstrate the sound accuracy and performance of the proposed method. For Poisson problems in R-2 and R-3, we establish that linearly complete generalized barycentric interpolants deliver optimal rates of convergence in the L-2-norm and the H-1-seminorm. (literal)

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