Weighted error estimates for finite element solutions of variational inequalities

In this note the studies begun in Blum and Suttmeier (1999) on adaptive fin ite element discretisations for nonlinear problems described by Variational inequalities are continued. Similar to the concept proposed, e.g., in Beck er and Rannacher (1996) for variational equalities, weighted a posteriori e stimates for controlling arbitrary functionals of the discretisation error are constructed by using a duality argument. Numerical results for the obst acle problem demonstrate the derived error bounds to be reliable and, used for an adaptive grid refinement strategy, to produce economical meshes.