A Superconvergence result for mixed finite element approximations of the eigenvalue problem

Abstract

In this paper, we present a superconvergence result for the mixed finite element approxima- tions of general second order elliptic eigenvalue problems. It is known that a superconvergence result has been given by Duran et al. (Math. Models Methods Appl. Sci. 9 (1999) 1165-1178) and Gardini (ESAIM: M2AN 43 (2009) 853-865) for the lowest order Raviart-Thomas approximation of Laplace eigenvalue problems. In this work, we introduce a new way to derive the superconvergence of general second or- der elliptic eigenvalue problems by general mixed finite element methods which have the commuting diagram property. Some numerical experiments are given to confirm the theoretical analysis.