DFG
FAU Erlangen-Nuremberg

Numerical Analysis and Discretization Strategies for Optimal Control Problems with Singularities

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Project leaders

Institut für Mathematik und Bauinformatik, Fakultät für Bauingenieur- und Vermessungswesen
Universität der Bundeswehr München

Tel: 089 6004-3405
Fax: 089 6004-4136


Email: thomas.apel@unibw.de

Homepage: http://www.unibw.de/bauv1/personen/apel/


Universität Duisburg-Essen
Fachbereich Mathematik
D-47048 Duisburg

Fax: 0203 379-2117
Phone: 0203 379-2669

Email: arnd.roesch@uni-due.de Homepage: [1]


Zentrum Mathematik, M1
TU München
Boltzmannstr. 3
85748 Garching

phone: +49 (089) 289 17938
fax: +49 (089) 289 17932

Email: vexler@ma.tum.de homepage: http://www.ricam.oeaw.ac.at/people/page/vexler/

DFG funded assistant

Martin Naß (Uni Duisburg-Essen)
martin.nass@uni-due.de

Johannes Pfefferer (UniBw München)
johannes.pfefferer@unibw.de

Max Winkler (Institut)
max.winkler@unibw.de

FWF funded assistant

Olaf Benedix (TU München)
benedix@ma.tum.de

Assistants

Thomas Flaig (UniBw München)
thomas.flaig@unibw.de

Dominik Meidner (TU München)

Description

Optimization of technological processes plays an increasing role in science and engineering. This project deals with different types of optimal control problems governed by elliptic or parabolic partial differential equations and characterized by additional pointwise inequality constraints for control and state. Of particular interest are problems with all kinds of singularities including those due to reentrant corners and edges, nonsmooth coefficients, small parameters, and inequality constraints.

The project targets two goals: First, starting from a priori error estimates, families of meshes are generated that ensure optimal approximation rates. Second, reliable posteriori error estimators are developed and used for adaptive mesh refinement. A challenge is the incorporation of pointwise inequality constraints for control and state. Both techniques can ensure efficient and reliable numerical results. With a successful strategy it is possible to calculate numerical solutions of the optimal control problems with given accuracy at low cost.

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