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The mimetic finite difference method on polygonal meshes for diffusion-type problems

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Abstract

New mimetic discretizations of diffusion-type equations (for instance, equations modeling single phase Darcy flow in porous media) on unstructured polygonal meshes are derived. The first order convergence rate for the fluid velocity and the second-order convergence rate for the pressure on polygonal, locally refined and non-matching meshes are demonstrated with numerical experiments.

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Authors and Affiliations

  1. Department of Mathematics, University of Houston, Houston, TX, 77204, USA

    Y. Kuznetsov

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

    K. Lipnikov & M. Shashkov

Authors
  1. Y. Kuznetsov
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  2. K. Lipnikov
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  3. M. Shashkov
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Correspondence to K. Lipnikov.

Additional information

The work was partly performed at Los Alamos National Laboratory operated by the University of California for the US Department of Energy under contract W-7405-ENG-36. The U.S. Government’s right to retain a non-exclusive, royalty free license in and to any copyright is acknowledged. The research of the first author was supported by a grant from the Los Alamos Computer Science Institute (LACSI).

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Kuznetsov, Y., Lipnikov, K. & Shashkov, M. The mimetic finite difference method on polygonal meshes for diffusion-type problems. Comput Geosci 8, 301–324 (2004). https://doi.org/10.1007/s10596-004-3771-1

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  • DOI: https://doi.org/10.1007/s10596-004-3771-1

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