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Block Jacobi for Discontinuous Galerkin Discretizations: No Ordinary Schwarz Methods

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Domain Decomposition Methods in Science and Engineering XXI

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 98))

Abstract

For classical discretizations of elliptic partial differential equations, like conforming finite elements or finite differences, block Jacobi methods are equivalent to classical Schwarz methods with Dirichlet transmission conditions. This is however not necessarily the case for discontinuous Galerkin methods (DG). We will show for the model problem \(-\varDelta u = f\) and various DG discretizations that a block Jacobi method applied to the discretized problem can be interpreted as a Schwarz method with different transmission conditions.

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References

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Acknowledgements

We would like to thank BLANCA AYUSO for her useful comments.

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Authors and Affiliations

  1. Université de Genève, 2-4 rue du Lièvre, CP 64, CH-1211, Genève 4, Switzerland

    Martin J. Gander & Soheil Hajian

Authors
  1. Martin J. Gander
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  2. Soheil Hajian
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Corresponding author

Correspondence to Soheil Hajian .

Editor information

Editors and Affiliations

  1. INRIA, Rennes, France

    Jocelyne Erhel

  2. Section de Mathématiques, Université de Genève, Genève, Switzerland

    Martin J. Gander

  3. Laboratoire Analyse, Géometrie & Applications, Université Paris XIII, Villetaneuse, France

    Laurence Halpern

  4. INRIA, Rennes, France

    Géraldine Pichot

  5. Laboratoire LMNO, Université de Caen, Caen, France

    Taoufik Sassi

  6. New York University Courant Institute, New York, New York, USA

    Olof Widlund

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© 2014 Springer International Publishing Switzerland

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Gander, M.J., Hajian, S. (2014). Block Jacobi for Discontinuous Galerkin Discretizations: No Ordinary Schwarz Methods. In: Erhel, J., Gander, M., Halpern, L., Pichot, G., Sassi, T., Widlund, O. (eds) Domain Decomposition Methods in Science and Engineering XXI. Lecture Notes in Computational Science and Engineering, vol 98. Springer, Cham. https://doi.org/10.1007/978-3-319-05789-7_27

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