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We introduce a discontinuous Galerkin method for the mixed formulation of theelasticity eigenproblem with reduced symmetry. The analysis of the resultingdiscrete eigenproblem does not fit in the standard spectral approximationframework since the underlying source operator is not compact and the scheme isnonconforming. We show that the proposed scheme provides a correctapproximation of the spectrum and prove asymptotic error estimates for theeigenvalues and the eigenfunctions. Finally, we provide several numerical teststo illustrate the performance of the method and confirm the theoreticalresults.

Mixed discontinuous Galerkin approximation of the elasticity eigenproblem