Advances in Difference Equations
Volume 2006 (2006), Article ID 85807, 10 pages
Maximum norm analysis of an overlapping nonmatching grids method for the obstacle problem
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.
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 norm.