Journal of Applied Mathematics
Volume 2011 (2011), Article ID 605140, 18 pages
http://dx.doi.org/10.1155/2011/605140
Research Article

Maximum Norm Analysis of a Nonmatching Grids Method for Nonlinear Elliptic PDES

A. Harbi1 and M. Boulbrachene2

1Departement De Mathematiques, Universite Badji Mokhtar, Annaba 23000, Algeria
2Department of Mathematics & Statistics, Sultan Qaboos University, Muscat 123, Oman

Received 14 June 2011; Revised 9 September 2011; Accepted 14 September 2011

Academic Editor: M. A. Fontelos

Copyright © 2011 A. Harbi and M. Boulbrachene. 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 two overlapping subdomains with nonmatching grids. We consider a domain which is the union of two overlapping subdomains where each subdomain has its own independently generated grid. The two meshes being mutually independent on the overlap region, a triangle belonging to one triangulation does not necessarily belong to the other one. Under a Lipschitz asssumption on the nonlinearity, we establish, on each subdomain, an optimal 𝐿 ∞ error estimate between the discrete Schwarz sequence and the exact solution of the PDE.