First-order system least squares for linear elasticity: Numerical results

Two first-order system least squares (FOSLS) methods based on L-2 norms are applied to various boundary value problems of planar linear elasticity. Bo th use finite element discretization and multigrid solution methods. They a re two-stage algorithms that solve rst for the displacement flux variable ( the gradient of displacement, which easily yields the deformation and stres s variables), then for the displacement variable itself. As a complement to a companion theoretical paper, this paper focuses on numerical results, in cluding finite element accuracy and multigrid convergence estimates that co n rm uniform optimal performance even as the material tends to the incompre ssible limit.