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Pre-Publicación 2012-06

Salim Meddahi, David Mora, Rodolfo Rodríguez:

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

Abstract:

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 and prove quasi-optimal error estimates. Finally, we report some numerical experiments.

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Esta prepublicacion dio origen a la(s) siguiente(s) publicación(es) definitiva(s):

Salim MEDDAHI, David MORA, Rodolfo RODRíGUEZ: Finite element spectral analysis for the mixed formulation of the elasticity equations. SIAM Journal on Numerical Analysis, vol. 51, 2, pp. 1041-1063, (2013).