A simple and efficient Hellinger-Reissner type mixed finite element for nearly incompressible elasticity

The mixed finite element method is a promising approach in order to overcome locking phenomena of classical displacement based finite elements in the (nearly) incompressible regime for the elasticity problem. In this work we present a novel element based on Hellinger-Reissner's principle for linear elasticity. Essential for the construction of the element is a restriction of the solution space for the stresses, resulting in a formulation with displacements in H1(B) and stresses in H(div,B). The symmetry of the stresses is achieved in a weak sense, without the necessity of additional degrees of freedom. This formulation leads for the case of lowest order interpolation to a very efficient and robust finite element, even satisfying the numerical inf-sup test in two and three dimensions.