Time finite elements and error computation for (visco)plasticity with hardening or softening

In this paper we investigate the possibility for, and characteristics of, reliable and e cient a posteriori error computation at the integration of the constitutive relations pertinent to (visco)plasticity with softening=hardening. The variational structure admits the use of nite elements in time, which are based on the Discontinuous Galerkin method. An important feature is the possibility to select ‘goal-oriented’ error measures with great freedom. A key task is to identify and solve an auxiliary problem, that is the dual of the actual (primal) problem. Di erent strategies for computing the dual solution accurately, yet avoiding excessive cost, are investigated in the paper. In particular, we consider the characteristics at the limit of rate-independent plasticity