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Additive Schwarz Methods for Elliptic Mortar Finite Element Problems

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Summary.

Two variants of the additive Schwarz method for solving linear systems arising from the mortar finite element discretization on nonmatching meshes of second order elliptic problems with discontinuous coefficients are designed and analyzed. The methods are defined on subdomains without overlap, and they use special coarse spaces, resulting in algorithms that are well suited for parallel computation. The condition number estimate for the preconditioned system in each method is proportional to the ratio H/h, where H and h are the mesh sizes, and it is independent of discontinuous jumps of the coefficients. For one of the methods presented the choice of the mortar (nonmortar) side is independent of the coefficients.

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Authors and Affiliations

  1. Institute for Informatics, University of Bergen, N-5020, Bergen, Norway

    Petter E. Bjørstad

  2. Department of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Maksymilian Dryja

  3. Institute for Mathematics, University of Augsburg, Universitätsstr. 14, D-86159, Augsburg, Germany

    Talal Rahman

Authors
  1. Petter E. Bjørstad
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  2. Maksymilian Dryja
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  3. Talal Rahman
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Corresponding author

Correspondence to Petter E. Bjørstad.

Additional information

This work has been supported in part by the Norwegian Research Council, grant 113492/420

This work has been supported in part by the National Science Foundation, grant NSF-CCR-9732208 and in part by the Polish Science Foundation, grant 2P03A02116

Mathematics Subject Classification (2000): 65N55

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Bjørstad, P., Dryja, M. & Rahman, T. Additive Schwarz Methods for Elliptic Mortar Finite Element Problems. Numer. Math. 95, 427–457 (2003). https://doi.org/10.1007/s00211-002-0429-6

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  • DOI: https://doi.org/10.1007/s00211-002-0429-6

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