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

TL;DR

This paper analyzes the spectral properties of a finite element least-squares method for linear elasticity, revealing dependence on material parameters and mesh, despite robustness in incompressible limits.

Contribution

It provides detailed spectral analysis and numerical results for a least-squares finite element approach to linear elasticity, highlighting parameter and mesh sensitivities.

Findings

Spectrum depends strongly on Lamé parameters

Method remains robust in incompressible limit

Numerical results illustrate spectral sensitivities

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.