Mimetic finite difference method (Articolo in rivista)

Type
Label
  • Mimetic finite difference method (Articolo in rivista) (literal)
Anno
  • 2014-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1016/j.jcp.2013.07.031 (literal)
Alternative label
  • Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail (2014)
    Mimetic finite difference method
    in Journal of computational physics (Print)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail (literal)
Pagina inizio
  • 1163 (literal)
Pagina fine
  • 1227 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://www.sciencedirect.com/science/article/pii/S0021999113005135 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 257 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#pagineTotali
  • 65 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • PB (literal)
Note
  • ISI Web of Science (WOS) (literal)
  • Scopu (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Applied Mathematics and Plasma Physics Group, T-5, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, United States; Methods and Algorithms Group, XCP-4, X-Computational Physics Division, Los Alamos National Laboratory, Los Alamos, NM, United States (literal)
Titolo
  • Mimetic finite difference method (literal)
Abstract
  • The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathematical identities of the vector and tensor calculus. This article is the first comprehensive review of the 50-year long history of the mimetic methodology and describes in a systematic way the major mimetic ideas and their relevance to academic and real-life problems. The supporting applications include diffusion, electromagnetics, fluid flow, and Lagrangian hydrodynamics problems. The article provides enough details to build various discrete operators on unstructured polygonal and polyhedral meshes and summarizes the major convergence results for the mimetic approximations. Most of these theoretical results, which are presented here as lemmas, propositions and theorems, are either original or an extension of existing results to a more general formulation using polyhedral meshes. Finally, flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems. (C) 2013 Elsevier Inc. All rights reserved. (literal)
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