A new primal-mixed finite element method for the linear elasticity problem

Abstract

We introduced a new augmented variational formulation for the elasticity problem in the plane that involves four unknowns, namely, the displacement, the stress tensor, the strain tensor of small deformations and the pressure. We proved that this problem is well posed for appropriate values of a stabilization parameter. We also gave sufficient conditions for the well posedness of the corresponding Galerkin scheme, and detailed concrete examples of discrete spaces satisfying these conditions. We provided error estimates for these cases.