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.

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Author:Michael HintermüllerGND, Ronald H. W. HoppeORCiDGND
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/1280
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2009-16)
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