Weighted Error Estimates for Finite Element Solutions of Variational Inequalities

摘要

In this note the studies begun in Blum and Suttmeier (l999) on adaptive finite element discretisations for nonlinear problems described by variational inequalities are continued. Similar to the concept proposed, e.g.. in Becker and Rannacher (1996) for variational equalities, weighted a posteriori esti- mates for controlling arbitrary functionals of the discretisation error are constructed by using a duality argument. Numcrical results for the obstacle problem demonstrate the derived error bounds to be reliable and, used for an adaptive grid refinement strategy, to producc economical meshes.