A least squares method for linear elasticity using a patch reconstructed space

Abstract

We propose a discontinuous least squares finite element method for solving the linear elasticity. The approximation space is obtained by patch reconstruction with only one unknown per element. We apply the L2 norm least squares principle with the weak imposition of the continuity across the interior faces to the stress–displacement formulation. The optimal convergence order under the energy norm is attained. Numerical results of the linear elasticity are presented to verify the error estimates. Our method enjoys the advantages of discontinuous Galerkin methods, and in addition we illustrate the great simplicity in implementation, the robustness and the improved efficiency of our method.