Goal-oriented adaptivity in pointwise state constrained optimal control of partial differential equations

  • Primal-dual-weighted goal-oriented a posteriori error estimates for pointwise state constrained optimal control problems for second order elliptic partial differential equations are derived. The constraints give rise to a primal-dual weighted error term representing the mismatch in the complementarity system due to discretization. In the case of sufficiently regular active (or coincidence) sets and problem data, a further decomposition of the multiplier into a regular L2-part on the active set and a singular part concentrated on the boundary between the active and inactive set allows to further characterize the mismatch error. The paper ends by a report on the behavior of the error estimates for test cases including the case of singular active sets consisting of smooth curves or points, only.

Download full text files

Export metadata

Statistics

Number of document requests

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Michael HintermüllerGND, Ronald H. W. HoppeGND
URN:urn:nbn:de:bvb:384-opus4-10801
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/1280
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2009-16)
Type:Preprint
Language:English
Publishing Institution:Universität Augsburg
Contributing Corporation:University of Houston, Humboldt Universität Berlin, Universität Graz
Release Date:2009/06/25
Tag:optimal control; state constraints; mesh adaptivity; a posteriori error analysis; goal oriented dual weighted residuals
GND-Keyword:Elliptische Differentialgleichung; Optimale Kontrolle; Fehleranalyse; A-posteriori-Abschätzung
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
Licence (German):Deutsches Urheberrecht mit Print on Demand