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Convergence analysis of the high-order mimetic finite difference method

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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.

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Authors and Affiliations

  1. Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, via Saldini 50, 20133, Milano, Italy

    L. Beirão da Veiga

  2. Los Alamos National Laboratory, Theoretical Division, MS B284, Los Alamos, NM, 87545, USA

    K. Lipnikov

  3. Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI), CNR, via Ferrata 1, 27100, Pavia, Italy

    G. Manzini

Authors
  1. L. Beirão da Veiga
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  2. K. Lipnikov
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  3. G. Manzini
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Correspondence to L. Beirão da Veiga.

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Beirão da Veiga, L., Lipnikov, K. & Manzini, G. Convergence analysis of the high-order mimetic finite difference method. Numer. Math. 113, 325–356 (2009). https://doi.org/10.1007/s00211-009-0234-6

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  • DOI: https://doi.org/10.1007/s00211-009-0234-6

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