| Issue |
ESAIM: M2AN
Volume 46, Number 5, September-October 2012
|
|
|---|---|---|
| Page(s) | 1107 - 1120 | |
| DOI | https://doi.org/10.1051/m2an/2011076 | |
| Published online | 13 February 2012 | |
A priori error estimates for a state-constrained elliptic optimal control problem
1
Universität Duisburg-Essen, Fakultät für Mathematik, Forsthausweg 2,
47057
Duisburg,
Germany
arnd.roesch@uni-due.de
2
Universität Stuttgart, Institut für Angewandte Analysis und
Numerische Simulation, Pfaffenwaldring 57, 70569
Stuttgart,
Germany
simeon.steinig@ians.uni-stuttgart.de
Received:
18
November
2010
Revised:
5
October
2011
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.
Mathematics Subject Classification: 49J20 / 35B45
Key words: Elliptic optimal control problem / state constraint / a priori error estimates
© EDP Sciences, SMAI, 2012
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