| Issue |
ESAIM: COCV
Volume 20, Number 2, April-June 2014
|
|
|---|---|---|
| Page(s) | 416 - 441 | |
| DOI | https://doi.org/10.1051/cocv/2013069 | |
| Published online | 07 March 2014 | |
A certified reduced basis method for parametrized elliptic optimal control problems∗
1
Aachen Institute for Advanced Study in Computational Engineering
Science (AICES), RWTH Aachen University, Schinkelstraße 2,
52062
Aachen,
Germany
kaercher@aices.rwth-aachen.de
2
Numerical Mathematics, RWTH Aachen University, Templergraben
55, 52056
Aachen,
Germany
grepl@igpm.rwth-aachen.de
Received:
25
May
2012
Revised:
24
April
2013
In this paper, we employ the reduced basis method as a surrogate model for the solution of linear-quadratic optimal control problems governed by parametrized elliptic partial differential equations. We present a posteriori error estimation and dual procedures that provide rigorous bounds for the error in several quantities of interest: the optimal control, the cost functional, and general linear output functionals of the control, state, and adjoint variables. We show that, based on the assumption of affine parameter dependence, the reduced order optimal control problem and the proposed bounds can be efficiently evaluated in an offline-online computational procedure. Numerical results are presented to confirm the validity of our approach.
Mathematics Subject Classification: 49K20 / 49M29 / 35J25 / 65N15 / 65K05 / 93C20
Key words: Optimal control / reduced basis method / a posteriori error estimation / model order reduction / parameter-dependent systems
© EDP Sciences, SMAI, 2014
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