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.