摘要
In recent years,a nonoverlapping domain decomposition iterative procedure,which is based on using Robin-type boundary conditions as information transmission conditions on the subdomain interfaces,has been developed and analyzed.It is known that the convergence rate of this method is 1-O(h),where h is mesh size.In this paper,the convergence rate is improved to be 1-O(h1/2 H-1/2)sometime by choosing suitable parameter,where H is the subdomain size.Counter examples are constructed to show that our convergence estimates are sharp,which means that the convergence rate cannot be better than 1-O(h1/2H-1/2)in a certain case no matter how parameter is chosen.
In recent years, a nonoverlapping domain decomposition iterative procedure, which is based on using Robin-type boundary conditions as information transmission conditions on the subdomain interfaces, has been developed and analyzed. It is known that the convergence rate of this method is 1 ? O(h), where h is mesh size. In this paper, the convergence rate is improved to be 1 ? O(h 1/2H?1/2) sometime by choosing suitable parameter, where H is the subdomain size. Counter examples are constructed to show that our convergence estimates are sharp, which means that the convergence rate cannot be better than 1 ? O(h 1/2H?1/2) in a certain case no matter how parameter is chosen.
基金
the National Basic Research Program of China(Grant No.2005CB321701)
the National Natural Science Foundation of China(Grant No.10731060)
