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.

Keywords: adaptive finite element method, C-stationarity, goal-oriented error estimation, mathematical programming with equilibrium constraints, optimal control of variational inequalities

@article{COCV_2014__20_2_524_0, author = {Hinterm\"uller, M. and Hoppe, R. H. W. and L\"obhard, C.}, title = {Dual-weighted goal-oriented adaptive finite elements for optimal control of elliptic variational inequalities}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {524--546}, publisher = {EDP-Sciences}, volume = {20}, number = {2}, year = {2014}, doi = {10.1051/cocv/2013074}, mrnumber = {3264215}, zbl = {1287.49030}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2013074/} }

TY - JOUR AU - Hintermüller, M. AU - Hoppe, R. H. W. AU - Löbhard, C. TI - Dual-weighted goal-oriented adaptive finite elements for optimal control of elliptic variational inequalities JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2014 SP - 524 EP - 546 VL - 20 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2013074/ DO - 10.1051/cocv/2013074 LA - en ID - COCV_2014__20_2_524_0 ER -

%0 Journal Article %A Hintermüller, M. %A Hoppe, R. H. W. %A Löbhard, C. %T Dual-weighted goal-oriented adaptive finite elements for optimal control of elliptic variational inequalities %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 524-546 %V 20 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2013074/ %R 10.1051/cocv/2013074 %G en %F COCV_2014__20_2_524_0

Hintermüller, M.; Hoppe, R. H. W.; Löbhard, C. Dual-weighted goal-oriented adaptive finite elements for optimal control of elliptic variational inequalities. ESAIM: Control, Optimisation and Calculus of Variations, Volume 20 (2014) no. 2, pp. 524-546. doi : 10.1051/cocv/2013074. http://archive.numdam.org/articles/10.1051/cocv/2013074/

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