Weighted error estimates for finite element solutions of variational inequalities (Q1592534)

The authors continue the studies begun in their earlier paper [Caleolo 37, No. 2, 65-77 (2000; Zbl 0954.65053)] on adaptive finite element discretisations for nonlinear problems described by variational inequalities. Similar to the concept proposed by \textit{R. Becker} and \textit{R. Rannacher} [East-West J. Numer. Math. 4, No. 4, 237-264 (1996; Zbl 0868.65076)] for variational equalities, weighted a posteriori estimates for controlling arbitrary functionals of the discretisation error are constructed by using a duality argument. Numerical results for the obstacle problem demonstrate the derived error bounds to be reliable and to produce economical meshes.