Numerische Mathematik

, Volume 113, Issue 3, pp 325–356

Convergence analysis of the high-order mimetic finite difference method

Article

DOI: 10.1007/s00211-009-0234-6

Cite this article as:
Beirão da Veiga, L., Lipnikov, K. & Manzini, G. Numer. Math. (2009) 113: 325. doi:10.1007/s00211-009-0234-6
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Abstract

We prove second-order convergence of the conservative variable and its flux in the high-order MFD method. The convergence results are proved for unstructured polyhedral meshes and full tensor diffusion coefficients. For the case of non-constant coefficients, we also develop a new family of high-order MFD methods. Theoretical result are confirmed through numerical experiments.

Mathematics Subject Classification (2000)

65N12

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Dipartimento di Matematica “F. Enriques”Università degli Studi di MilanoMilanoItaly
  2. 2.Los Alamos National Laboratory, Theoretical DivisionLos AlamosUSA
  3. 3.Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI), CNRPaviaItaly