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

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

ESAIM: Control, Optimisation and Calculus of Variations (2014)

- Volume: 20, Issue: 2, page 524-546
- ISSN: 1292-8119

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topHintermüller, M., Hoppe, R. H. W., and Löbhard, C.. "Dual-weighted goal-oriented adaptive finite elements for optimal control of elliptic variational inequalities." ESAIM: Control, Optimisation and Calculus of Variations 20.2 (2014): 524-546. <http://eudml.org/doc/272881>.

@article{Hintermüller2014,

abstract = {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.},

author = {Hintermüller, M., Hoppe, R. H. W., Löbhard, C.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {adaptive finite element method; C-stationarity; goal-oriented error estimation; mathematical programming with equilibrium constraints; optimal control of variational inequalities; optimal control; variational inequalities; mathematical programming; equilibrium constraints},

language = {eng},

number = {2},

pages = {524-546},

publisher = {EDP-Sciences},

title = {Dual-weighted goal-oriented adaptive finite elements for optimal control of elliptic variational inequalities},

url = {http://eudml.org/doc/272881},

volume = {20},

year = {2014},

}

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

PB - EDP-Sciences

VL - 20

IS - 2

SP - 524

EP - 546

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/272881

ER -

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