A mortar mimetic finite difference method on non-matching grids

  • Authors:

  • Markus Berndt;Konstantin Lipnikov;Mikhail Shashkov;Mary F. Wheeler;Ivan Yotov

  • Affiliations:

  • Los Alamos National Laboratory, Mail Stop B284, 87545, Los Alamos, NM, USA;Los Alamos National Laboratory, Mail Stop B284, 87545, Los Alamos, NM, USA;Los Alamos National Laboratory, Mail Stop B284, 87545, Los Alamos, NM, USA;Institute for Computational Engineering and Sciences (ICES), Department of Aerospace Engineering and Engineering Mechanics, and Department of Petroleum and Geosystems Engineering, The University o ...;Department of Mathematics, University of Pittsburgh, Mail Stop B284, 301 Thackeray Hall, 15260, Pittsburgh, PA, USA

  • Venue:
  • Numerische Mathematik
  • Year:
  • 2005

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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.