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A Simple Uniformly Convergent Iterative Method for the Non-symmetric Incomplete Interior Penalty Discontinuous Galerkin Discretization

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Domain Decomposition Methods in Science and Engineering XIX

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 78))

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Abstract

We introduce a uniformly convergent iterative method for the systems arising from non-symmetric IIPG linear approximations of second order elliptic problems. The method can be viewed as a block Gauß–Seidel method in which the blocks correspond to restrictions of the IIPG method to suitably constructed subspaces. Numerical tests are included, showing the uniform convergence of the iterative method in an energy norm.

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Acknowledgments

First author was supported by MEC grants MTM2008-03541 and HI2008-0173. The work of the second author was supported in part by the National Science Foundation NSF-DMS 0511800 and NSF-DMS 0810982.

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Authors and Affiliations

  1. Departamento de Matemáticas, Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Universidad Autónoma de Madrid, Madrid, 28049, Spain

    Blanca Ayuso

  2. Department of Mathematics, Penn State University, University Park, PA, 16802, USA

    Ludmil T. Zikatanov

Authors
  1. Blanca Ayuso
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  2. Ludmil T. Zikatanov
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Corresponding author

Correspondence to Blanca Ayuso .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, Xiangtan University, Xiangtan, 411105, China, People's Republic

    Yunqing Huang

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

    Ralf Kornhuber

  3. Department of Mathematics, Courant Institute of Math. Sciences, New York University, Mercer St. 251, New York, 10012, New York, USA

    Olof Widlund

  4. Eberly College of Science, Dept. Mathematics, Pennsylvania State University, University Park, 16802, Pennsylvania, USA

    Jinchao Xu

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Ayuso, B., Zikatanov, L.T. (2011). A Simple Uniformly Convergent Iterative Method for the Non-symmetric Incomplete Interior Penalty Discontinuous Galerkin Discretization. In: Huang, Y., Kornhuber, R., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XIX. Lecture Notes in Computational Science and Engineering, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11304-8_38

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