On the spectrum of an operator associated with least-squares finite elements for linear elasticity

Abstract: In this paper we provide some more details on the numerical analysis and we present some enlightening numerical results related to the spectrum of a finite element least-squares approximation of the linear elasticity formulation introduced recently. We show that, although the formulation is robust in the incompressible limit for the source problem, its spectrum is strongly dependent on the Lam\'e parameters and on the underlying mesh.