Open Access

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

Advances in Difference Equations20062006:085807

DOI: 10.1155/ADE/2006/85807

Received: 11 July 2005

Accepted: 26 September 2005

Published: 16 March 2006

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.

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Authors’ Affiliations

(1)
Department of Mathematics, College of Science, Sultan Qaboos University
(2)
Departement de Mathematiques Faculte des Sciences, Universite Badji Mokhtar

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Copyright

© M. Boulbrachene and S. Saadi 2006

This article is published under license to BioMed Central Ltd. 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.