The finite element approximation of optimal control problems for semilinear elliptic partial differential equation is considered, where the control belongs to a finite-dimensional set and state constraints are given in finitely many points of the domain. Under the standard linear independency condition on the active gradients and a strong second-order sufficient optimality condition, optimal error estimates are derived for locally optimal controls.
Mots-clés : finite element approximation, optimal control problem, finitely many pointwise state constraints
@article{M2AN_2010__44_1_167_0,
author = {Merino, Pedro and Tr\"oltzsch, Fredi and Vexler, Boris},
title = {Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {167--188},
publisher = {EDP-Sciences},
volume = {44},
number = {1},
year = {2010},
doi = {10.1051/m2an/2009045},
mrnumber = {2647757},
zbl = {1191.65076},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2009045/}
}
TY - JOUR AU - Merino, Pedro AU - Tröltzsch, Fredi AU - Vexler, Boris TI - Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2010 SP - 167 EP - 188 VL - 44 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2009045/ DO - 10.1051/m2an/2009045 LA - en ID - M2AN_2010__44_1_167_0 ER -
%0 Journal Article %A Merino, Pedro %A Tröltzsch, Fredi %A Vexler, Boris %T Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space %J ESAIM: Modélisation mathématique et analyse numérique %D 2010 %P 167-188 %V 44 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2009045/ %R 10.1051/m2an/2009045 %G en %F M2AN_2010__44_1_167_0
Merino, Pedro; Tröltzsch, Fredi; Vexler, Boris. Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space. ESAIM: Modélisation mathématique et analyse numérique, Tome 44 (2010) no. 1, pp. 167-188. doi : 10.1051/m2an/2009045. http://www.numdam.org/articles/10.1051/m2an/2009045/
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