  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 L 2 norm least
squares principle to the stress-displacement formulation based on discontinuous
approximation with normal continuity across the interior faces. The optimal
convergence order under the energy norm is attained. Numerical results of
linear elasticity are presented to verify the error estimates. In addition to
enjoying the advantages of discontinuous Galerkin method, we illustrate the
great simplicity in implementation, the robustness and the improved efficiency
of our method.
