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An adaptive finite element method is developed for a class of optimal control problems  with elliptic variational inequality constraints and objective functionals defined on the space  of continuous functions, necessitated by a point-tracking requirement with respect to the state  variable. A suitable first order stationarity concept is derived for the problem class via a penalty  technique. The dual-weighted residual approach for goal-oriented adaptive finite elements is  applied and relies on the stationarity system. It yields primal residuals weighted by approxi-  mate dual quantities and vice versa as well as complementarity mismatch errors. A report on  numerical tests, including the critical case of biactivity, completes this work.Peer Reviewe

Mesh adaptivity in optimal control of elliptic variational inequalities with point-tracking of the state