On the spectrum of the finite element approximation of a three field formulation for linear elasticity

Abstract

We continue the investigation on the spectrum of operators arising from the discretization of partial differential equations. In this paper we consider a three field formulation recently introduced for the finite element least-squares approximation of linear elasticity. We discuss in particular the distribution of the discrete eigenvalues in the complex plane and how they approximate the positive real eigenvalues of the continuous problem. The dependence of the spectrum on the Lamé parameters is considered as well and its behavior when approaching the incompressible limit.

Keywords

• Eigenvalue problem
• Linear elasticity
• Least-squares finite elements