Preprint 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.
This preprint gave rise to the following definitive publication(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).