First-order system least squares for the stress-displacement formulation: Linear elasticity

摘要

This paper develops a least-squares finite element method for linear elasticity in both two and three dimensions. The least-squares functional is based on the stress-displacement formulation with the symmetry condition of the stress tensor imposed in the first-order system. For the respective displacement and stress, using the Crouzeix - Raviart and Raviart - Thomas finite element spaces, our least-squares finite element method is shown to be optimal in the ( broken) H-1 and H(div) norms uniform in the incompressible limit. [References: 20]