A posteriori error analysis for two non-overlapping domain decomposition techniques

  • Authors:

  • C. Bernardi;T. Chacón Rebollo;E. Chacón Vera;D. Franco Coronil

  • Affiliations:

  • Laboratoire Jacques-Louis Lions, C.N.R.S. et Université Pierre et Marie Curie. Boite courrier 187, 4, Place Jussieu, 75252 Paris Cedex 05, France;Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla. C/Tarfia, s/n. 41080 Sevilla, Spain;Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla. C/Tarfia, s/n. 41080 Sevilla, Spain;Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla. C/Tarfia, s/n. 41080 Sevilla, Spain

  • Venue:
  • Applied Numerical Mathematics
  • Year:
  • 2009

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Abstract

This paper is devoted to the construction of fast solvers for penalty domain decomposition techniques, based upon a posteriori error analysis. We introduce a penalty non-overlapping domain decomposition method (ddm) motivated by the a posteriori error analysis of the method proposed by Chacon and Chacon in [T. Chacon Rebollo, E. Chacon Vera, A non-overlapping domain decomposition method for the Stokes equations via a penalty term on the interface, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 1-16]. In the new method a H"0"0^1^/^2(@C) penalty term replaces the L^2(@C) one in the original method. The number of iterations needed by the new ddm to yield a solution with an error of the same order as the discretization error is remarkably reduced. We develop an a posteriori error analysis that we use to determine an optimal value of the penalty parameter for a given grid, and also to jointly determine an optimal grid and a penalty parameter to reduce the error below a targeted value. Several numerical tests for model problems exhibit the good performances of our approach and provide to a numerical comparison of the two penalty methods.