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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.

Finite Element Spectral Analysis for the Mixed Formulation of the Elasticity Equations