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.