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Journal of Applied Mathematics
Volume 2012, Article ID 947085, 15 pages
http://dx.doi.org/10.1155/2012/947085
Research Article

A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition Methods

Department of Mathematics, Badji Mokhtar University, B.P. 12, Annaba 23000, Algeria

Received 8 June 2012; Revised 18 September 2012; Accepted 21 November 2012

Academic Editor: Malgorzata Peszynska

Copyright © 2012 Hakima Benlarbi and Ahmed-Salah Chibi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A posteriori error estimates for the generalized overlapping domain decomposition method (GODDM) (i.e., with Robin boundary conditions on the interfaces), for second order boundary value problems, are derived. We show that the error estimate in the continuous case depends on the differences of the traces of the subdomain solutions on the interfaces. After discretization of the domain by finite elements we use the techniques of the residual a posteriori error analysis to get an a posteriori error estimate for the discrete solutions on subdomains. The results of some numerical experiments are presented to support the theory.