Additive Schwarz methods for the Crouzeix-Raviart mortar finite element for elliptic problems with discontinuous coefficients

  • Authors:

  • Talal Rahman;Xuejun Xu;Ronald Hoppe

  • Affiliations:

  • Bergen Center for Computational Science, University of Bergen, Thormøhlensgt. 55, 5008, Bergen, Norway;LSEC, Institute of Computational Mathematics, Chinese Academy of Sciences, P.O.Box 2719, Thormøhlensgt. 55, 100080, Beijing, People's Republic of China;Department of Mathematics, University of Houston, P.O.Box 2719, Calhoun Street, TX77204-3008, Houston, USA and Institute of Mathematics, University of Augsburg, Universitätsstr. 14, 86159, ...

  • Venue:
  • Numerische Mathematik
  • Year:
  • 2005

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Abstract

In this paper, we propose two variants of the additive Schwarz method for the approximation of second order elliptic boundary value problems with discontinuous coefficients, on nonmatching grids using the lowest order Crouzeix-Raviart element for the discretization in each subdomain. The overall discretization is based on the mortar technique for coupling nonmatching grids. The convergence behavior of the proposed methods is similar to that of their closely related methods for conforming elements. The condition number bound for the preconditioned systems is independent of the jumps of the coefficient, and depend linearly on the ratio between the subdomain size and the mesh size. The performance of the methods is illustrated by some numerical results.