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A Posteriori Error Analysis of Penalty Domain Decomposition Methods for Linear Elliptic Problems

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • C. Bernardi

    (C.N.R.S. et Université Pierre et Marie Curie, Laboratoire Jacques-Louis Lions)

  • T. Chacón Rebollo

    (Universidad de Sevilla, Departamento de Ecuaciones Diferenciales y Análisis Numérico)

  • E. Chacón Vera

    (Universidad de Sevilla, Departamento de Ecuaciones Diferenciales y Análisis Numérico)

  • D. Franco Coronil

    (Universidad de Sevilla, Departamento de Ecuaciones Diferenciales y Análisis Numérico)

Abstract

In this work we introduce a new version of the non-overlapping domain decomposition method (DDM) method proposed by Chacón and Chacón in [5]. In the new method a H 00 1/2 (Γ) penalty term replaces the L2(Γ) one in the original method. We develop a posteriori error analysis, aimed to design strategies for optimizing the combined choice of the penalty parameter and the adaptation of the grid, to reduce the computational cost. We shall discuss the computational benefits of using H 00 1/2 (Γ) penalty versus L2(Γ) penalty.

Suggested Citation

  • C. Bernardi & T. Chacón Rebollo & E. Chacón Vera & D. Franco Coronil, 2008. "A Posteriori Error Analysis of Penalty Domain Decomposition Methods for Linear Elliptic Problems," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 373-380, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_44
    DOI: 10.1007/978-3-540-69777-0_44
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