Convergence of the mimetic finite difference method for eigenvalue problems in mixed form

Abstract

Optimal convergence rates for the mimetic finite difference method applied to eigenvalue problems in mixed form are proved. The analysis is based on a new a priori error bound for the source problem and relies on the existence of an appropriate elemental lifting of the mimetic discrete solution. Compared to the original convergence analysis of the method, the new a priori estimate does not require any extra regularity assumption on the right-hand side of the source problem. Numerical results confirming the optimal behavior of the method are presented.