Advances in Difference Equations
Volume 2006 (2006), Article ID 85807, 10 pages
doi:10.1155/ADE/2006/85807

Maximum norm analysis of an overlapping nonmatching grids method for the obstacle problem

M. Boulbrachene1 and S. Saadi2

1Department of Mathematics, College of Science, Sultan Qaboos University, P.O. Box 36, Muscat 123, Oman
2Departement de Mathematiques, Faculte des Sciences, Universite Badji Mokhtar, Annaba BP 12, Algeria

Received 11 July 2005; Revised 24 September 2005; Accepted 26 September 2005

Copyright © 2006 M. Boulbrachene and S. Saadi. 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 an overlapping Schwarz method on nonmatching grids for second-order elliptic obstacle problem. We consider a domain which is the union of two overlapping subdomains where each subdomain has its own independently generated grid. The grid points on the subdomain boundaries need not match the grid points from the other subdomain. Under a discrete maximum principle, we show that the discretization on each subdomain converges quasi-optimally in the L∞ norm.