DFG
FAU Erlangen-Nuremberg

Model Reduction by Adaptive Discretization in Optimal Control

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Project leader

Institut für Angewandte Mathematik
Uni Heidelberg

Tel: 06221 54-4873
Tel: 06221 54-6170 (Sekr.)
Fax: 06221 54-5634

Email: rannacher@iwr.uni-heidelberg.de

Homepage:

DFG funded assistant

Michael Geiger (Uni Heidelberg)
michael.geiger@iwr.uni-heidelberg.de

Anke Griesbaum (Uni Heidelberg)
anke.griesbaum@iwr.uni-heidelberg.de

former DFG funded assistant

Winnifried Wollner (Uni Heidelberg)
winnifried.wollner@iwr.uni-heidelberg.de

Description

This project will employ the concept of 'goal-oriented' adaptivity for model 'reduction' in solving optimal control problems governed by partial differential equations (PDE). The underlying framework is the 'Dual Weighted Residual (DWR) method' wich was originally developed by R. Becker and R. Rannacher for adaptive discretization of PDE by the finite element Galerkin method. In this approach residual-based 'weighted' a posteriori error estimates are derived for quantities interest, where the weights are obtained by numerically solving an associated 'dual problem'. Due to the use of problem inherent sensitivity information, these a posteriori error estimates are tailored to the special needs of the computation. This allows for successively improved control of spatial and time discretization which eventually results in highly economical discretization. In this project the main emphasis is on nonstationary optimal control problems, which pose particularly high requirements on computational resources, and on problems invlolving additional constraints for controls and states. In these cases model reduction by adaptive discretization may prove most usefull. Research on these topics in the context of PDE-constrained optimal control has started only recently and there are still many theoretical as well as practical open questions.

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