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.
Mots-clés : elliptic optimal control problem, state constraint, a priori error estimates
@article{M2AN_2012__46_5_1107_0,
author = {R\"osch, Arnd and Steinig, Simeon},
title = {\protect\emph{A priori }error estimates for a state-constrained elliptic optimal control problem},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1107--1120},
publisher = {EDP-Sciences},
volume = {46},
number = {5},
year = {2012},
doi = {10.1051/m2an/2011076},
zbl = {1271.65104},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2011076/}
}
TY - JOUR AU - Rösch, Arnd AU - Steinig, Simeon TI - A priori error estimates for a state-constrained elliptic optimal control problem JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 1107 EP - 1120 VL - 46 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2011076/ DO - 10.1051/m2an/2011076 LA - en ID - M2AN_2012__46_5_1107_0 ER -
%0 Journal Article %A Rösch, Arnd %A Steinig, Simeon %T A priori error estimates for a state-constrained elliptic optimal control problem %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 1107-1120 %V 46 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2011076/ %R 10.1051/m2an/2011076 %G en %F 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 , Tome 46 (2012) no. 5, pp. 1107-1120. doi : 10.1051/m2an/2011076. http://www.numdam.org/articles/10.1051/m2an/2011076/
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