Dipl.-math. oec. Gunter Winkler

Control constrained optimal control problems in non-convex three dimensional polyhedral domains

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http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800626

Kurzfassung in Englisch

The work selects a specific issue from the numerical analysis of
optimal control problems. We investigate a linear-quadratic optimal
control problem based on a partial differential equation on
3-dimensional non-convex domains. Based on efficient solution methods
for the partial differential equation an algorithm known from control
theory is applied. Now the main objectives are to prove that there is
no degradation in efficiency and to verify the result by numerical
experiments.

We describe a solution method which has second order convergence,
although the intermediate control approximations are piecewise
constant functions. This superconvergence property is gained from a
special projection operator which generates a piecewise constant
approximation that has a supercloseness property, from a sufficiently
graded mesh which compensates the singularities introduced by the
non-convex domain, and from a discretization condition which
eliminates some pathological cases.

Both isotropic and anisotropic discretizations are investigated and
similar superconvergence properties are proven.

A model problem is presented and important results from the regularity
theory of solutions to partial differential equation in non-convex
domains have been collected in the first chapters. Then a collection
of statements from the finite element analysis and corresponding
numerical solution strategies is given. Here we show newly developed
tools regarding error estimates and projections into finite element
spaces. These tools are necessary to achieve the main results. Known
fundamental statements from control theory are applied to the given
model problems and certain conditions on the discretization are
defined. Then we describe the implementation used to solve the model
problems and present all computed results.

weitere Metadaten

Schlagwörter
anisotropic finite elements
Schlagwörter
linear-quadratic optimal control problem
Schlagwörter
non-convex domain
Schlagwörter
superconvergence
SWD SchlagworteAnisotropes Gitter
SWD SchlagworteElliptische Differentialgleichung
SWD SchlagworteFinite-Elemente-Methode
SWD SchlagworteOptimale Kontrolle
DDC Klassifikation510
Institution(en) 
HochschuleTU Chemnitz
FakultätFakultät für Mathematik
BetreuerProf. Dr. rer. nat. habil. Thomas Apel
GutachterProf. Dr. rer. nat. habil. Thomas Apel
Prof. Dr. rer. nat. habil. Bernd Heinrich
Prof. Dr. rer. nat. habil. Christian Großmann
DokumententypDissertation
SpracheEnglisch
Tag d. Einreichung (bei der Fakultät)29.11.2007
Tag d. Verteidigung / Kolloquiums / Prüfung20.03.2008
Veröffentlichungsdatum (online)28.05.2008
persistente URNurn:nbn:de:bsz:ch1-200800626
Externe Referenzhttp://www.guwi17.de/diss/index.html
URL

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