Functional a Posteriori Error Estimates for Incremental Models in Elasto-plasticity

We consider a convex variational problem related to a time-step problem in elasto-plastic models with isotropic hardening. Our goal it to derive a posteriori error estimate of the difference between the exact solution and any function in the admissible (energy) class of the problem considered. The estimates are obtained by a advanced version of the variational approach earlier used for linear boundary-value problems and nonlinear variational problems with convex functionals (see [20, 21] and the monography [18]). They do no contain mesh-dependent constants and are valid for any conforming approximations regardless of the method used for their derivation. It is shown that the structure of error majorant reflects properties of the exact solution so that the majorant vanishes only if an approximate solution coincides with the exact one. Moreover, it possesses necessary continuity properties, so that any sequence of approximations converging to the exact solution in the energy space generates a sequence of positive numbers (explicitly computable by the majorant functional) that tends to zero.