Mixed finite elements of least-squares type for elasticity

In terms of stress and displacement, the linear elasticity problem is discretized by a least-squares finite element method. In the case of a convex polygonal domain, the stress is approximated by the lowest-order Raviart-Thomas-Nédélec flux element, and the displacement by the linear C0 element. We obtain coerciveness and optimal H1, L2 and H(div)-error bounds, uniform in Lamé constant λ, for displacement and stress, respectively. Our method also allows the use of any other combination of conforming elements for stress and displacement, e.g., C0 elements for all variables.