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
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.