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, Volume 44 (2010) no. 1, p. 167-188

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.

DOI : https://doi.org/10.1051/m2an/2009045
Classification:  49J20,  35B37
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {44},
number = {1},
year = {2010},
pages = {167-188},
doi = {10.1051/m2an/2009045},
zbl = {1191.65076},
mrnumber = {2647757},
language = {en},
url = {http://www.numdam.org/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, Volume 44 (2010) no. 1, pp. 167-188. doi : 10.1051/m2an/2009045. http://www.numdam.org/item/M2AN_2010__44_1_167_0/

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