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Domain Decomposition Methods in Science and Engineering pp 345–352Cite as

A FETI-DP Method for the Mortar Discretization of Elliptic Problems with Discontinuous Coefficients

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 40))

Summary

Second order elliptic problems with discontinuous coefficients are considered. The problem is discretized by the finite element method on geometrically conforming non-matching triangulations across the interface using the mortar technique. The resulting discrete problem is solved by a FETI-DP method. We prove that the method is convergent and its rate of convergence is almost optimal and independent of the jumps of coefficients. Numerical experiments for the case of four subregions are reported. They confirm the theoretical results.

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References

  • C. Bernardi, Y. Maday, and A. T. Patera. A new non conforming approach to domain decomposition: The mortar element method. In H. Brezis and J.-L. Lions, editors, Collége de France Seminar. Pitman, 1994. This paper appeared as a technical report about five years earlier.

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  • M. Dryja and W. Proskurowski. On preconditioners for mortar discretization of elliptic problems. Numerical Linear Algebra with Applications, 10:65–82, 2003.

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  • M. Dryja and O. Widlund. A FETI-DP method for a mortar discretization of elliptic problems. In P. L. and T. A., editors, Recent developments in domain decomposition methods, pages 41–52. Springer Verlag, 2002.

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  • M. Dryja and O. Widlund. A generalized FETI-DP method for the mortar discretization of elliptic problems. In I. H. et al., editor, Fourteenth International Conference in Domain Decomposition methods, pages 27–38. UNAM, Mexico City, Mexico, 2003.

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Author information

Authors and Affiliations

  1. Mathematics, Informatics and Mechanics, Warsaw University, Warsaw

    Maksymilian Dryja

  2. Mathematics, University of Southern California, California

    Wlodek Proskurowski

Authors
  1. Maksymilian Dryja
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  2. Wlodek Proskurowski
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Editor information

Editors and Affiliations

  1. Moffett Field, CA

    Timothy J. Barth

  2. Bonn

    Michael Griebel

  3. New York

    David E. Keyes  & Tamar Schlick  & 

  4. Espoo

    Risto M. Nieminen

  5. Leuven

    Dirk Roose

  6. Fachbereich Mathematik und Informatik, Freie Universität Berlin, Arnimallee 2-6, 14195, Berlin, Germany

    Ralf Kornhuber

  7. Department of Mathematics, University of Houston, Philip G. Hoffman Hall 651, 77204-3008, Houston, TX, USA

    Ronald Hoppe

  8. Dassault Aviation, 78 Quai Marcel Dassault Cedex 300, 92552, St. Cloud, France

    Jacques Périaux

  9. Laboratoire Jacques-Louis Lions, Université Paris VI, 175 Rue de Chevaleret, 75013, Paris, France

    Olivier Pironneau

  10. Courant Institute of Mathematical Science, New York University, Mercer Street 251, 10012, New York, USA

    Olof Widlund

  11. Department of Mathematics Eberly College of Science, Pennsylvania Sate University, McAllister Building 218, 16802, University Park, PA, USA

    Jinchao Xu

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© 2005 Springer-Verlag Berlin Heidelberg

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Dryja, M., Proskurowski, W. (2005). A FETI-DP Method for the Mortar Discretization of Elliptic Problems with Discontinuous Coefficients. In: Barth, T.J., et al. Domain Decomposition Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26825-1_34

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