ERROR ESTIMATES FOR THE ULTRA WEAK VARIATIONAL FORMULATION IN LINEAR ELASTICITY

作者：Luostari Teemu^*; Huttunen Tomi; Monk Peter

来源：ESAIM: Mathematical Modelling and Numerical Analysis , 2013, 47(1): 183-211.

DOI：10.1051/m2an/2012025

• Ultra weak variational formulation
• error estimates
• plane wave basis
• linear elasticity
• upwind discontinuous Galerkin method

We prove error estimates for the ultra weak variational formulation (UWVF) in 3D linear elasticity. We show that the UWVF of Navier%26apos;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 L-2 (Omega) norm in terms of the best approximation error. Our final result is an L-2 (Omega) norm error estimate using approximation properties of plane waves to give an estimate for the order of convergence. Numerical examples are presented.

• 出版日期2013-1