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A priori error estimates for astate-constrained elliptic optimal control problem

Published online by Cambridge University Press:  13 February 2012

Arnd Rösch  and
Simeon Steinig
Arnd Rösch
Affiliation:
Universität Duisburg-Essen, Fakultät für Mathematik, Forsthausweg 2, 47057 Duisburg, Germany. arnd.roesch@uni-due.de
Simeon Steinig
Affiliation:
Universität Stuttgart, Institut für Angewandte Analysis und Numerische Simulation, Pfaffenwaldring 57, 70569 Stuttgart, Germany; simeon.steinig@ians.uni-stuttgart.de

Abstract

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We examine an elliptic optimal control problem with control and state constraints inℝ3. An improved error estimate of 𝒪(hs) with 3/4 ≤ s ≤ 1 − ε is proven for a discretisationinvolving piecewise constant functions for the control and piecewise linear for the state.The derived order of convergence is illustrated by a numerical example.

Keywords

Elliptic optimal control problemstate constrainta priori error estimates

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 5 , September 2012 , pp. 1107 - 1120
Copyright
© EDP Sciences, SMAI, 2012

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