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On the convergence of generalized Schwarz algorithms for solving obstacle problems with elliptic operators

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Abstract

In this paper, multiplicative and additive generalized Schwarz algorithms for solving obstacle problems with elliptic operators are developed and analyzed. Compared with the classical Schwarz algorithms, in which the subproblems are coupled by the Dirichlet boundary conditions, the generalized Schwarz algorithms use Robin conditions with parameters as the transmission conditions on the interface boundaries. As a result, the convergence rate can be speeded up by choosing Robin parameters properly. Convergence of the algorithms is established.

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Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, 410082, China

    Gaojie Chen & Jinping Zeng

  2. Dongguan University of Technology, Dongguan, China

    Jinping Zeng

Authors
  1. Gaojie Chen
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  2. Jinping Zeng
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Corresponding author

Correspondence to Jinping Zeng.

Additional information

This work was supported by 973 national project of China (2004CB719402) and by national nature science foundation of China (10671060).

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Chen, G., Zeng, J. On the convergence of generalized Schwarz algorithms for solving obstacle problems with elliptic operators. Math Meth Oper Res 67, 455–469 (2008). https://doi.org/10.1007/s00186-007-0206-5

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  • DOI: https://doi.org/10.1007/s00186-007-0206-5

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