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

Emmanuel Creusé (1) , Serge Nicaise (2)

1 SIMPAF - SImulations and Modeling for PArticles and Fluids
2 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

In this paper, we consider a discretization method proposed by Wieners and Wohlmuth [26] (see also [16]) for second order operators, which is a coupling between a mixed method in a sub-domain 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.

Mots clés: A posteriori estimates; coupled method

Domaines: Analyse numérique [math.NA]

Emmanuel Creusé, Serge Nicaise. A posteriori error estimations of a coupled mixed and standard Galerkin method for second order operators. Journal of Computational and Applied Mathematics, 2008, 213 (1), pp.35-55. ⟨10.1016/j.cam.2006.12.027⟩. ⟨hal-00768642⟩