Arbitrary-order nodal mimetic discretizations of elliptic problems on polygonal meshes (Articolo in rivista)

Type
Label
  • Arbitrary-order nodal mimetic discretizations of elliptic problems on polygonal meshes (Articolo in rivista) (literal)
Anno
  • 2011-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1137/100807764 (literal)
Alternative label
  • Beirao da Veiga L., Lipnikov K., Manzini G. (2011)
    Arbitrary-order nodal mimetic discretizations of elliptic problems on polygonal meshes
    in SIAM journal on numerical analysis (Print); Society for Industrial and Applied Mathematics, Philadelphia, PA (Stati Uniti d'America)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Beirao da Veiga L., Lipnikov K., Manzini G. (literal)
Pagina inizio
  • 1737 (literal)
Pagina fine
  • 1760 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://epubs.siam.org/doi/abs/10.1137/100807764 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 49 (literal)
Rivista
Note
  • Scopu (literal)
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Dipartimento di Matematica, Università di Milano; Los Alamos Natl Lab, Los Alamos, USA; Istituto di Matematica Applicata e Tecnologie Informatiche, CNR, Pavia (literal)
Titolo
  • Arbitrary-order nodal mimetic discretizations of elliptic problems on polygonal meshes (literal)
Abstract
  • We develop and analyze a new family of mimetic methods on unstructured polygonal meshes for the diffusion problem in primal form. These methods are derived from the local consistency condition that is exact for polynomials of any degree m >= 1. The degrees of freedom are (a) solution values at the quadrature nodes of the Gauss-Lobatto formulas on each mesh edge, and (b) solution moments inside polygons. The convergence of the method is proven theoretically and an optimal error estimate is derived in a mesh-dependent norm that mimics the energy norm. Numerical experiments confirm the convergence rate that is expected from the theory. (literal)
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