Uniform convergence and preconditioning method for mortar mixed element method for nonselfadjoint and indefinite problems Original Research Article

In this paper, a mortar version of the modified mixed element method is proposed for nonselfadjoint and indefinite second-order elliptic problems. It is proven that the modified mortar mixed element method is equivalent to a modified mortar nonconforming element method. Based on this equivalence, the existence, uniqueness and uniform convergence of the solution for the modified mortar mixed element method are shown under minimal regularity assumption. Meanwhile an optimal error estimate for the modified mortar mixed element method is obtained under H2 smoothness assumption. Furthermore an additive Schwarz preconditioning method for solving the discrete problem is provided and the nearly optimal convergence rate for the preconditioned GMRES method is proven under the minimal regularity assumption.