On Interior Penalty And Mixed Discontinuous Galerkin Methods For Elasticity

In this paper, we review existing discontinuous Galerkin (DG) methods for elasticity and introduce a new formulation based on mixed finite elements. We highlight the subtle and important differences between Interior Penalty (IP) and mixed FEM based methods. In the mixed method for elasticity, choices of function spaces for approximating primal and dual variable is non-trivial for two main reasons, namely the compatibility between the two spaces (inf − sup condition) and a symmetry condition for functions interpolating the stress tensor in such a space. We will discuss and address these issues and prove that the resulting mixed scheme is coercive and consistent and leads to a formulation which is simple, extremely robust and optimally convergent in global norms.