Uniform convergence and Schwarz method for the mortar projection nonconforming and mixed element methods for nonselfadjoint and indefinite problems Original Research Article

In this paper, two mortar versions of the so-called projection nonconforming and the mixed element methods are proposed, respectively, for nonselfadjoint and indefinite second-order elliptic problems. It is proven that the mortar mixed element method is equivalent to the mortar projection nonconforming element method. Based on this equivalence, the existence, uniqueness, and uniform convergence of the solution for mortar mixed element method are shown only under minimal regularity assumption. Meanwhile, the optimal error estimate is obtained under certain regularity assumption. Furthermore, an additive Schwarz preconditioning method is proposed for solving the discrete problem and the nearly optimal convergence rate for the preconditioned GMRES method is proven under minimal regularity assumption. Finally, the practical implementation of the method is adderssed and numerical experiments are presented.