Geodesic
Dual-weighted goal-oriented adaptive finite elements for optimal control of elliptic variational inequalities
ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 2, pp. 524-546

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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.

DOI : 10.1051/cocv/2013074
Classification : 49M25, 65K15, 90C33
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://geodesic.mathdoc.fr/articles/10.1051/cocv/2013074/}
}
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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, Tome 20 (2014) no. 2, pp. 524-546. doi: 10.1051/cocv/2013074

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