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Non-overlapping Domain Decomposition for the Richards Equation via Superposition Operators

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Domain Decomposition Methods in Science and Engineering XVIII

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 70))

Summary

Simulations of saturated-unsaturated groundwater flow in heterogeneous soil can be carried out by considering non-overlapping domain decomposition problems for the Richards equation in subdomains with homogeneous soil. By the application of different Kirchhoff transformations in the different subdomains local convex minimization problems can be obtained which are coupled via superposition operators on the interface between the subdomains. The purpose of this article is to provide a rigorous mathematical foundation for this reformulation in a weak sense. In particular, this involves an analysis of the Kirchhoff transformation as a superposition operator on Sobolev and trace spaces.

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References

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik und Informatik, Freie Universität Berlin, Berlin, Germany

    Heiko Berninger

Authors
  1. Heiko Berninger
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Corresponding author

Correspondence to Heiko Berninger .

Editor information

Editors and Affiliations

  1. School of Computer Science and Engineering, The Hebrew University of Jerusalem, Ross Building - Givat Ram Campus, 91904, Jerusalem, Israel

    Michel Bercovier

  2. Section de mathématiques, Université de Genève, 2-4 rue du Lièvre, 1211, Genève 24, Switzerland

    Martin J. Gander

  3. Institut für Mathematik, Freie Universität Berlin, Arnimallee 6, 14195, Berlin-Dahlem, Germany

    Ralf Kornhuber

  4. Courant Institute, 251 Mercer Street, New York, NY, 10012, USA

    Olof Widlund

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Berninger, H. (2009). Non-overlapping Domain Decomposition for the Richards Equation via Superposition Operators. In: Bercovier, M., Gander, M.J., Kornhuber, R., Widlund, O. (eds) Domain Decomposition Methods in Science and Engineering XVIII. Lecture Notes in Computational Science and Engineering, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02677-5_17

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