A unified approach for handling convection terms in finite volumes and mimetic discretization methods for elliptic problems (Articolo in rivista)

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  • A unified approach for handling convection terms in finite volumes and mimetic discretization methods for elliptic problems (Articolo in rivista) (literal)
Anno
  • 2011-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1093/imanum/drq018 (literal)
Alternative label
  • Beirao da Veiga L., Droniou J., Manzini G. (2011)
    A unified approach for handling convection terms in finite volumes and mimetic discretization methods for elliptic problems
    in IMA journal of numerical analysis; Oxford University Press, Oxford (Regno Unito)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Beirao da Veiga L., Droniou J., Manzini G. (literal)
Pagina inizio
  • 1357 (literal)
Pagina fine
  • 1401 (literal)
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  • http://imajna.oxfordjournals.org/content/31/4/1357 (literal)
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  • 31 (literal)
Rivista
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  • 4 (literal)
Note
  • ISI Web of Science (WOS) (literal)
  • Scopu (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Dipartimento di Matematica F. Enriques, Università Degli Studi di Milano; Institut de Mathématiques et de Modélisation de Montpellier, Université Montpellier ; Istituto di Matematica Applicata e Tecnologie Informatiche - CNR, Pavia. (literal)
Titolo
  • A unified approach for handling convection terms in finite volumes and mimetic discretization methods for elliptic problems (literal)
Abstract
  • We study the numerical approximation to the solution of the steady convection-diffusion equation. The diffusion term is discretized by using the hybrid mimetic method (HMM), which is the unified formulation for the hybrid finite-volume (FV) method, the mixed FV method and the mimetic finite-difference method recently proposed in Droniou et al. (2010, Math. Models Methods Appl. Sci., 20, 265-295). In such a setting we discuss several techniques to discretize the convection term that are mainly adapted from the literature on FV or FV schemes. For this family of schemes we provide a full proof of convergence under very general regularity conditions of the solution field and derive an error estimate when the scalar solution is in H 2(?). Finally, we compare the performance of these schemes on a set of test cases selected from the literature in order to document the accuracy of the numerical approximation in both diffusion- and convection-dominated regimes. Moreover, we numerically investigate the behaviour of these methods in the approximation of solutions with boundary layers or internal regions with strong gradients. (literal)
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