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Recent Advances in Domain Decomposition Methods for the Stokes Problem

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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))

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Abstract

Domain decomposition methods for the Stokes problem are developed under a more general framework, which allows both continuous and discontinuous pressure functions and more flexibility in the construction of the coarse problem. For the case of discontinuous pressure functions, a coarse problem related to only primal velocity unknowns is shown to give scalability in both dual and primal types of domain decomposition methods. The two formulations are shown to have the same extreme eigenvalues and the ratio of the two extreme eigenvalues weakly depends on the local problem size. This property results in a good scalability in both the primal and dual formulations for the case with discontinuous pressure functions. The primal formulation can also be applied to the case with continuous pressure functions and various numerical experiments are carried out to present promising features of our approach.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Kyung Hee University, Yongin, Korea

    Hyea Hyun Kim

  2. Department of Mathematical Sciences, KAIST, Daejeon, Korea

    Chang-Ock Lee

  3. National Institute of Mathematical Sciences, Daejeon, Korea

    Eun-Hee Park

Authors
  1. Hyea Hyun Kim
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  2. Chang-Ock Lee
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  3. Eun-Hee Park
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Corresponding author

Correspondence to Hyea Hyun Kim .

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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Kim, H.H., Lee, CO., Park, EH. (2014). Recent Advances in Domain Decomposition Methods for the Stokes Problem. 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_5

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