Adaptive numerical analysis in primal elastoplasticity with hardening Original Research Article

The quasi-static viscoplastic resp. elastoplastic evolution problem with isotropic or kinematic hardening is considered with emphasis on optimal convergence and adapted mesh-refining in the spatial discretization. Within one time-step of an implicit time-discretization, the finite element method leads to a minimisation problem for non-smooth convex functions on discrete subspaces. For piecewise constant resp. affine ansatz functions, the stress resp. displacement approximations are experimentally and theoretically shown to converge linearly. An a posteriori error estimate then justifies an automatic adaptive mesh-refining algorithm. Numerical examples support the superiority of the adapted mesh.