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

We present a posteriori error estimators and adaptive methods for the finit e element approximation of nonlinear problems and especially elastoplastici ty. The main characteristic of the proposed method is the introduction of d uality techniques or in other notions the reciprocal theorem. For error est imation at an equilibrium point the non-linear boundary value problem and a n additional linearized dual problem are considered. The loading of the dua l problem is specifically designed for capturing the influence of the error s of the entire domain to the considered variable. Our approach leads to ea sy computable refinement indicators for locally or integrally defined varia bles. For instationary problems as elastoplasticity, in a first step, we ne glect the errors due to time discretization, and evaluate the error indicat ors within each time step for a stationary problem. The versatility of the presented framework is demonstrated with numerical examples. Copyright (C) 2000 John Wiley & Sons, Ltd.