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.
@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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {44},
year = {2010},
pages = {167-188},
doi = {10.1051/m2an/2009045},
mrnumber = {2647757},
zbl = {1191.65076},
language = {en},
url = {http://dml.mathdoc.fr/item/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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 44 (2010) pp. 167-188. doi : 10.1051/m2an/2009045. http://gdmltest.u-ga.fr/item/M2AN_2010__44_1_167_0/
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