The Brezzi–Pitkäranta stabilization scheme for the elasticity problem

In this paper, we consider the elasticity problem based on the Hellinger–Reissner variational principle. We use the equal order linear and bilinear mixed finite element spaces to approximate the stress and the displacement, and develop a Brezzi–Pitkäranta stabilization method for the finite element space pairs to overcome the lack of the inf–sup condition, then we give the error estimates of the stabilization approximation scheme. At last, we implement two numerical examples to test the stability and effectiveness of the proposed method.