Adaptive finite elements in elastoplasticity with mechanical error indicators and Neumann-type estimators

Abstract Many interesting tasks in technology need the solution of complex boundary value problems modeled by the mathematical theory of elasticity and elastoplasticity. Error controlled adaptive strategies should be used in order to achieve a prescribed accuracy of the computed solutions at minimum cost. In this paper, locally computed residual error indicators in the primal form of the finite-element-method for Elasticity as well as Hencky- and Prandtl-Reus-plasticity without and with nonlinear hardening are presented, controlling global errors of equilibrium, plastic strain rates, the yield condition and the numerical integration of the flow rule. Furthermore, an error estimator based on local Neumann problems is extended to elastoplasticity, based on improved boundary tractions. This recovery technique is called PEM (Posterior Equilibrium Method).