An adaptive finite element scheme for the Hellinger--Reissner elasticity mixed eigenvalue problem

Abstract

In this paper we study the approximation of eigenvalues arising from the mixed Hellinger--Reissner elasticity problem by using the simple finite element using partial relaxation of $C^0$ vertex continuity of stresses introduced recently by Jun Hu and Rui Ma. We prove that the method converge when a residual type error estimator is considered and that the estimator decays optimally with respect to the number of degrees of freedom.