Functional approach to a posteriori error estimation for elliptic optimal control problems with distributed control

  • We present a new approach to the a posteriori analysis of distributed optimal control problems. It is based on functional type a posteriori estimates that provide computable and guaranteed bounds of errors for any conforming approximations of a boundary value problem. We derive computable two-sided a posteriori estimates for the cost functional and estimates for the approximations of state and control functions. Numerical results illustrate efficiency of the approach suggested.

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Metadaten
Author:Alexandra GaevskayaGND, Ronald H. W. HoppeGND, Sergey I. Repin
URN:urn:nbn:de:bvb:384-opus4-4282
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/527
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2007-12)
Type:Preprint
Language:English
Publishing Institution:Universität Augsburg
Contributing Corporation:Steklov Institute of Mathematics, St. Petersburg
Release Date:2007/07/12
Tag:functional error majorants; distributed optimal control
GND-Keyword:Optimale Kontrolle; A-posteriori-Abschätzung; Fehleranalyse; Randwertproblem
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik