A posteriori error estimation of finite element approximations of pointwise state constrained distributed control problems

We provide an a posteriori error analysis of finite element approximations of pointwise state constrained distributed optimal control problems for second order elliptic boundary value problems. In particular, we derive a residual-type a posteriori error estimator and prove its efficiency and reliability up to oscillations in the data of the problem and a consistency error term. In contrast to the case of pointwise control constraints, the analysis is more complicated, since the multipliers associated with the state constraints live in measure spaces. The analysis essentially makes use of appropriate regularizations of the multipliers both in the continuous and in the discrete regime. Numerical examples are given to illustrate the performance of the error estimator.

Metadaten
Author:	Ronald H. W. Hoppe ORCiD GND, Michael Kieweg GND
URN:	urn:nbn:de:bvb:384-opus4-4351
Frontdoor URL	https://opus.bibliothek.uni-augsburg.de/opus4/541
Series (Serial Number):	Preprints des Instituts für Mathematik der Universität Augsburg (2007-16)
Type:	Preprint
Language:	English
Publishing Institution:	Universität Augsburg
Contributing Corporation:	Department of Mathematics, University of Houston
Release Date:	2007/07/02
Tag:	optimal control; pointwise state constraints; adaptive finite element methods
GND-Keyword:	Optimale Kontrolle; Finite-Elemente-Methode; A-posteriori-Abschätzung; Fehleranalyse; Elliptisches 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

Open Access