First-Order System Least Squares For Linear Elasticity: Numerical Results

Two first-order system least squares (FOSLS) methods based on L2 norms are applied to various boundary value problems of planar linear elasticity. Both use finite element discretization and multigrid solution methods. They are two-stage algorithms that solve first for the displacement flux variable (the gradient of displacement, which easily yields the deformation and stress variables), then for the displacement variable itself. As a complement to a companion theoretical paper, this paper focuses on numerical results, including finite element accuracy and multigrid convergence estimates that confirm uniform optimal performance---even as the material tends to the incompressible limit.