A posteriori error estimations of a coupled mixed and standard Galerkin method for second order operators

  • Authors:

  • Emmanuel Creusé;Serge Nicaise

  • Affiliations:

  • LAMAV, Université de Valenciennes et du Hainaut Cambrésis, 59313 Valenciennes Cedex 9, France and INRIA Futurs - Equipe SIMPAF, Université des Sciences et Technologies de Lille, Cit ...;LAMAV, Université de Valenciennes et du Hainaut Cambrésis, 59313 Valenciennes Cedex 9, France and INRIA Futurs - Equipe SIMPAF, Université des Sciences et Technologies de Lille, Cit ...

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2008

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Abstract

In this paper, we consider a discretization method proposed by Wieners and Wohlmuth [The coupling of mixed and conforming finite element discretizations, in: Domain Decomposition Methods, vol. 10, Contemporary Mathematics, vol. 218, American Mathematical Society, Providence RI, 1998, pp. 547-554] (see also [R.D. Lazarov, J. Pasciak, P.S. Vassilevski, Iterative solution of a coupled mixed and standard Galerkin discretization method for elliptic problems, Numer. Linear Algebra Appl. 8 (2001) 13-31]) for second order operators, which is a coupling between a mixed method in a subdomain and a standard Galerkin method in the remaining part of the domain. We perform an a posteriori error analysis of residual type of this method, by combining some arguments from a posteriori error analysis of Galerkin methods and mixed methods. The reliability and efficiency of the estimator are proved. Some numerical tests are presented and confirm the theoretical error bounds.