Finite element differential forms on curvilinear cubic meshes and their approximation properties (Articolo in rivista)

Type
Label
  • Finite element differential forms on curvilinear cubic meshes and their approximation properties (Articolo in rivista) (literal)
Anno
  • 2015-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1007/s00211-014-0631-3 (literal)
Alternative label
  • Douglas N. Arnold, Daniele Boffi, Francesca Bonizzoni (2015)
    Finite element differential forms on curvilinear cubic meshes and their approximation properties
    in Numerische Mathematik; Springer, Berlin Heidelberg (Germania)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Douglas N. Arnold, Daniele Boffi, Francesca Bonizzoni (literal)
Pagina inizio
  • 1 (literal)
Pagina fine
  • 20 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://link.springer.com/article/10.1007%2Fs00211-014-0631-3 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 129 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA; Dipartimento di Matematica \"F. Casorati\", Università di Pavia, 27100 Pavia, Italy; Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria (literal)
Titolo
  • Finite element differential forms on curvilinear cubic meshes and their approximation properties (literal)
Abstract
  • We study the approximation properties of a wide class of finite element differential forms on curvilinear cubic meshes in n dimensions. Specifically, we consider meshes in which each element is the image of a cubical reference element under a diffeomorphism, and finite element spaces in which the shape functions and degrees of freedom are obtained from the reference element by pullback of differential forms. In the case where the diffeomorphisms from the reference element are all affine, i.e., mesh consists of parallelotopes, it is standard that the rate of convergence in L^2 exceeds by one the degree of the largest full polynomial space contained in the reference space of shape functions. When the diffeomorphism is multilinear, the rate of convergence for the same space of reference shape function may degrade severely, the more so when the form degree is larger. The main result of the paper gives a sufficient condition on the reference shape functions to obtain a given rate of convergence. (literal)
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