Eigenvalue approximation by mixed non-conforming finite element methods

Abstract

In this paper we give a theory for the approximation of eigenvalue problems in mixed form by non-conforming methods. We then apply this theory to analyze the problem of determining the vibrational modes of a linear elastic structure using the classical Hellinger-Reissner mixed formulation. We show that a numerical method based on the lowest-order Arnold-Winther non-conforming space provides a spectrally correct approximation of the eigenvalue/eigenvector pairs. Moreover, the method is proven to converge with optimal order.