A-POSTERIORI ERROR CONTROL IN FINITE-ELEMENT METHODS VIA DUALITY TECHNIQUES - APPLICATION TO PERFECT PLASTICITY

In this paper a new technique for a posteriori error control and adapt ive mesh design is presented for finite element models in perfect plas ticity. The approach is based on weighted a posteriori error estimates derived by duality arguments as proposed in Becker and Rannacher (199 6) and Rannacher and Suttmeier (1997) for linear problems. The convent ional strategies for mesh refinement in finite element methods are mos tly based on a posteriori error estimates for the global energy norm i n terms of local residuals of the computed solution. These estimates r eflect the approximation properties of the trial functions by local in terpolation constants while the stability property of the continuous m odel enters through a global coercivity constant. However, meshes gene rated on the basis of such global error estimates are not appropriate in computing local quantities as point values or contour integrals and in the case of nonlinear material behavior. More accurate and efficie nt error estimation can be achieved by using suitable weights which ca n be obtained numerically in the course of the refinement process from the solutions of linearized dual problems. This feed-back approach is developed here for primal-mixed finite element models in linear-elast ic perfect plasticity.