tailieunhanh - Báo cáo hóa học: "MAXIMUM NORM ANALYSIS OF AN OVERLAPPING NONMATCHING GRIDS METHOD FOR THE OBSTACLE PROBLEM"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: MAXIMUM NORM ANALYSIS OF AN OVERLAPPING NONMATCHING GRIDS METHOD FOR THE OBSTACLE PROBLEM | MAXIMUM NORM ANALYSIS OF AN OVERLAPPING NONMATCHING GRIDS METHOD FOR THE OBSTACLE PROBLEM M. BOULBRACHENE AND S. SAADI Received 11 July 2005 Revised 24 September 2005 Accepted 26 September 2005 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. 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. 1. Introduction The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consists of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomain. Extensive analysis of Schwarz alternating method for continuous obstacle problem can be found in 8 9 . For convergence of discrete Schwarz algorithms of either additive or multiplicative types see for example 1 6 7 11 . In this paper we are interested in the error analysis in the maximum norm for the obstacle problem in the context of overlapping nonmatching grids we consider a domain D which is the union of two overlapping subdomains where each subdomain has its own triangulation. This kind of discretizations is very interesting as they can be applied to solving many practical problems which cannot be handled by global discretizations. They are earning particular attention of computational experts and engineers as