Uniform convergence and Schwarz method for the mortar element method for non-selfadjoint and indefinite problems

摘要

In this paper, the mortar element method for non-selfadjoint and indefinite second order elliptic problems is studied. Only under minimal regularity assumption, the existence, uniqueness and uniform convergence of the solution for the mortar element method are proven. Furthermore, an additive Schwarz preconditioning method is proposed and nearly optimal convergence rate for the preconditioned GMRES method is shown under minimal regularity assumption.