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

Abstract

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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.

How to cite

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Hintermüller, 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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