On the convergence rate of a parallel nonoverlapping domain decomposition method.

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. [ABSTRACT FROM AUTHOR]