Error estimates for the ultra weak variational formulation in linear elasticity∗
Department of Applied Physics, University of Eastern Finland P.O.
Box 1627, 70211
2 Department of Mathematical Sciences, University of Delaware, Newark, 19716 DE, USA.
Revised: 2 May 2012
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.
Mathematics Subject Classification: 65N15 / 65N30 / 74J05 / 74S30
Key words: Ultra weak variational formulation / error estimates / plane wave basis / linear elasticity / upwind discontinuous Galerkin method
© EDP Sciences, SMAI, 2012