A posteriori error estimation and adaptivity for elastoplasticity using the reciprocal theorem

We present a posteriori error estimators and adaptive methods for the nite element approximation of nonlinear problems and especially elastoplasticity. The main characteristic of the proposed method is the introduction of duality techniques or in other notions the reciprocal theorem. For error estimation at an equilibrium point the non-linear boundary value problem and an additional linearized dual problem are considered. The loading of the dual problem is speci cally designed for capturing the in uence of the errors of the entire domain to the considered variable. Our approach leads to easy computable re nement indicators for locally or integrally de ned variables. For instationary problems as elastoplasticity, in a rst step, we neglect the errors due to time discretization, and evaluate the error indicators within each time step for a stationary problem. The versatility of the presented framework is demonstrated with numerical examples