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Journal of Applied Mathematics
Volume 2013, Article ID 893182, 21 pages
http://dx.doi.org/10.1155/2013/893182
Research Article

Maximum Norm Analysis of an Arbitrary Number of Nonmatching Grids Method for Nonlinears Elliptic PDES

Department of Mathematics, Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, El Hadjar, 23000 Annaba, Algeria

Received 11 August 2013; Revised 7 October 2013; Accepted 9 October 2013

Academic Editor: Srinivasan Natesan

Copyright © 2013 Abida Harbi. 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

We provide a maximum norm analysis of a finite element Schwarz alternating method for a nonlinear elliptic PDE on an arbitrary number of overlapping subdomains with nonmatching grids. We consider a domain which is the union of an arbitrary number of overlapping subdomains where each subdomain has its own independently generated grid. The meshes being mutually independent on the overlap regions, a triangle belonging to one triangulation does not necessarily belong to the other ones. Under the a Lipschitz assumption on the nonlinearity, we establish, on each subdomain, an optimal error estimate between the discrete Schwarz sequence and the exact solution of the PDE.