Postprocessing for the Raviart--Thomas mixed finite element approximation of the eigenvalue problem

Abstract

In this paper we present a postprocessing scheme for the Raviart--Thomas mixed finite element approximation of the second order elliptic eigenvalue problem. This scheme is carried out by solving a primal source problem on a higher order space, and thereby can improve the convergence rate of the eigenfunction and eigenvalue approximations. It is also used to compute a posteriori error estimates which are asymptotically exact for the $L^2$ errors of the eigenfunctions. Some numerical results are provided to confirm the theoretical results.