Localised FE-analysis of Strang's problem based on Lagrange techniques

Abstract Performing numerical analysis in elastoplasticity, in several situations one observes plastic regions to cause difficulties in deriving nearly optimal error estimates under adequate regularity assumptions. In this note, for a typical model problem we propose an alternative estimate for the discretisation error localised to these critical parts. The discretisation error, measured locally in terms of stresses, is controlled by an a priori interpolation result and an a posteriori consistency estimate. The interpolation part possesses optimal order convergence in terms of the mesh size together with an adequate regularity assumption on the stresses. The consistency part is fully computable and does not contain heuristics.