Dual-weighted goal-oriented adaptive finite elements for optimal control of elliptic variational inequalities

Hintermüller, M.; Hoppe, R. H. W.; Löbhard, C.

ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 2, pp. 524-546.

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.

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