A posteriori error estimation and mesh adaptation for finite element models in elasto-plasticity

A new approach to a posteriori error estimation and adaptive mesh design based on techniques from optimal control is presented for primal-mixed finite element models in elasto-plasticity. This method uses global duality arguments for deriving weighted a posteriori error bounds for arbitrary functionals of the error representing physical quantities of interest. In these estimates local residuals of the computed solution are multiplied by certain weights which are obtained by solving a linearized global dual problem numerically. The resulting local error indicators are used in a feed-back process for generating economical meshes. This approach is developed here for the Hencky and Prandtl-Reuss models in linear-elastic perfect plasticity. Its performance is demonstrated for a plane-strain benchmark problem.