Finite element spectral analysis for the mixed formulation of the elasticity equations

Abstract:

We present an analysis of an 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 and prove quasi-optimal error estimates. Finally, we report some numerical experiments.