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A mortar mimetic finite difference method on non-matching grids

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Abstract

We consider mimetic finite difference approximations to second order elliptic problems on non-matching multiblock grids. Mortar finite elements are employed on the non-matching interfaces to impose weak flux continuity. Optimal convergence and, in certain cases, superconvergence is established for both the scalar variable and its flux. The theory is confirmed by computational results.

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Authors and Affiliations

  1. Los Alamos National Laboratory, Mail Stop B284, Los Alamos, NM, 87545, USA

    Markus Berndt, Konstantin Lipnikov & Mikhail Shashkov

  2. Institute for Computational Engineering and Sciences (ICES), Department of Aerospace Engineering and Engineering Mechanics, and Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, TX, 78712, USA

    Mary F. Wheeler

  3. Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA, 15260, USA

    Ivan Yotov

Authors
  1. Markus Berndt
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  2. Konstantin Lipnikov
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  3. Mikhail Shashkov
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  4. Mary F. Wheeler
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  5. Ivan Yotov
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Corresponding author

Correspondence to Markus Berndt.

Additional information

Supported by the US Department of Energy, under contractW-7405-ENG-36. LA-UR-04-4740.

Partially supported by NSF grants EIA 0121523 and DMS 0411413, by NPACI grant UCSD 10181410, and by DOE grant DE-FGO2-04ER25617.

Partially supported by NSF grants DMS 0107389, DMS 0112239 and DMS 0411694 and by DOE grant DE-FG02-04ER25618.

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Berndt, M., Lipnikov, K., Shashkov, M. et al. A mortar mimetic finite difference method on non-matching grids. Numer. Math. 102, 203–230 (2005). https://doi.org/10.1007/s00211-005-0631-4

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  • DOI: https://doi.org/10.1007/s00211-005-0631-4

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