Error estimates for the ultra weak variational formulation in linear elasticity

Abstract

We prove error estimates for the ultra weak variational formulation (UWVF) in 3D linear elasticity. We show that the UWVF of Navier’s equation can be derived as an upwind discontinuous Galerkin method. Using this observation, error estimates are investigated applying techniques from the theory of discontinuous Galerkin methods. In particular, we derive a basic error estimate for the UWVF in a discontinuous Galerkin type norm and then an error estimate in the L2 (Ω ) norm in terms of the best approximation error. Our final result is an L2 (Ω ) norm error estimate using approximation properties of plane waves to give an estimate for the order of convergence. Numerical examples are presented.