We examine an elliptic optimal control problem with control and state constraints in ℝ3. An improved error estimate of 𝒪(hs) with 3/4 ≤ s ≤ 1 - ε is proven for a discretisation involving piecewise constant functions for the control and piecewise linear for the state. The derived order of convergence is illustrated by a numerical example.
@article{M2AN_2012__46_5_1107_0,
author = {R\"osch, Arnd and Steinig, Simeon},
title = {A priori error estimates for a state-constrained elliptic optimal control problem},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {46},
year = {2012},
pages = {1107-1120},
doi = {10.1051/m2an/2011076},
zbl = {1271.65104},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2012__46_5_1107_0}
}
Rösch, Arnd; Steinig, Simeon. A priori error estimates for a state-constrained elliptic optimal control problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 46 (2012) pp. 1107-1120. doi : 10.1051/m2an/2011076. http://gdmltest.u-ga.fr/item/M2AN_2012__46_5_1107_0/
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