Convergence analysis of the high-order mimetic finite difference method

  • Authors:

  • L. Beirão da Veiga;K. Lipnikov;G. Manzini

  • Affiliations:

  • Università degli Studi di Milano, Dipartimento di Matematica “F. Enriques”, via Saldini 50, 20133, Milano, Italy;Los Alamos National Laboratory, Theoretical Division, MS B284, 87545, Los Alamos, NM, USA;Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI), CNR, via Ferrata 1, 27100, Pavia, Italy

  • Venue:
  • Numerische Mathematik
  • Year:
  • 2009

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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.