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Domain Decomposition Methods in Science and Engineering XIX pp 133–140Cite as

Discontinuous Galerkin and Nonconforming in Time Optimized Schwarz Waveform Relaxation

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

Abstract

In many fields of applications such as reactive transport or ocean-atmosphere coupling, models with very different spatial and time scales have to be coupled. Optimized Schwarz Waveform Relaxation methods (OSWR), applied to linear advection-reaction-diffusion problems in [1, 8], provide efficient solvers for this purpose. They have two main advantages: first, they are global in time and thus permit non conforming space-time discretization in different subdomains, and second, few iterations are needed to compute an accurate solution, due to optimized transmission conditions. It has been proposed in [4] to use a discontinuous Galerkin method in time as a subdomain solver. Rigorous analysis can be made for any degree of accuracy and local time-stepping, and finally time steps can be adaptively controlled by a posteriori error analysis, see [6, 7, 10].

* partially supported by french ANR (COMMA) and GdR MoMaS.

* partially supported by NSF Grant DMS-0504720

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Bibliography

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Author information

Authors and Affiliations

  1. LAGA, Université Paris XIII, 93430, Villetaneuse, France

    Laurence Halpern & Caroline Japhet*

  2. Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ, 08544-1000, USA

    Jérémie Szeftel*

  3. C.N.R.S., MAB, Université Bordeaux 1, 33405, Talence Cedex, France

    Jérémie Szeftel*

Authors
  1. Laurence Halpern
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  2. Caroline Japhet*
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  3. Jérémie Szeftel*
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Corresponding author

Correspondence to Laurence Halpern .

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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© 2011 Springer-Verlag Berlin Heidelberg

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Halpern, L., Japhet*, C., Szeftel*, J. (2011). Discontinuous Galerkin and Nonconforming in Time Optimized Schwarz Waveform Relaxation. 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_13

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