FINITE ELEMENT SPECTRAL ANALYSIS FOR THE MIXED FORMULATION OF THE ELASTICITY EQUATIONS

The aim of this paper is to analyze the linear elasticity eigenvalue problem formulated in terms of the stress tensor and the rotation. This is achieved by considering a mixed variational formulation in which the symmetry of the stress tensor is imposed weakly. We show that a discretization of the mixed eigenvalue elasticity problem with reduced symmetry based on the lowest order Arnold-Falk-Winther element provides a correct approximation of the spectrum. We also prove quasi-optimal error estimates. Finally, we report some numerical experiments.