A posteriori error estimates and domain decomposition with nonmatching grids |
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Authors: | Email author" target="_blank">J?PousinEmail author T?Sassi |
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Institution: | (1) MAPLY-INSA, CNRS UMR 5585, National Institute of Applied Sciences in Lyon, 20 av. A. Einstein, F-69621 Villeurbanne Cedex, France |
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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.
AMS subject classification 65J10, 65N55, 65M60T. 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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Keywords: | numerical analysis for PDE nonlinear elliptic problems a posteriori error estimates domain decomposition |
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