Numerical analysis of primal elastoplasticity with hardening

The quasi-static elastoplastic evolution problem with combined isotropic an d kinematic hardening is considered in its primal formulation with emphasis on improved optimal convergence of the lowest order scheme. Within one tim e-step of an implicit time-discretisation, the finite element method leads to a minimisation problem for non-smooth convex: functions on discrete subs paces. The internal variables can be eliminated such that the displacement is the only remaining variable. An priori error estimate is presented for t he fully-discrete method which proves linear convergence in space. Further, an a posteriori error estimate justifies an automatic adaptive mesh-refini ng algorithm. Numerical experiments confirm our theoretical predictions and the superiority of the adapted mesh.