Abstract
Let F be a nonlinear mapping defined from a Hilbert space X into its dual X′, and let x be in X the solution of F(x)=0. Assume that, a priori, the zone where the gradient of the function x has a large variation is known. The aim of this article is to prove a posteriori error estimates for the problem F(x)=0 when it is approximated with a Petrov–Galerkin finite element method combined with a domain decomposition method with nonmatching grids. A residual estimator for a model semi-linear problem is proposed. We prove that this estimator is asymptotically equivalent to a simplified one adapted to parallel computing. Some numerical results are presented, showing the practical efficiency of the estimator.
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Communicated by C.A. Micchelli
AMS subject classification
65J10, 65N55, 65M60
T. Sassi: Present address: Université de Caen, Laboratoire de Mathématiques Nicolas Oresme, UFR Sciences Campus II, Bd Maréchal Juin, 14032 Caen Cedex, France.
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Pousin, J., Sassi, T. A posteriori error estimates and domain decomposition with nonmatching grids. Adv Comput Math 23, 241–263 (2005). https://doi.org/10.1007/s10444-004-1779-7
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DOI: https://doi.org/10.1007/s10444-004-1779-7