A dual-weighted residual approach for goal-oriented adaptive finite elements for a class
of optimal control problems for elliptic variational inequalities is studied. The
development is based on the concept of C-stationarity. The overall error representation
depends on primal residuals weighted by approximate dual quantities and vice versa
as well as various complementarity mismatch errors. Also, a priori
bounds for C-stationary points and associated multipliers are derived. Details on
the numerical realization of the adaptive concept are provided and a report on numerical
tests including the critical cases of biactivity are presented.
