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A priori error estimates for finite elementdiscretizations of a shape optimization problem

Published online by Cambridge University Press:  07 October 2013

Bernhard Kiniger  and
Boris Vexler
Bernhard Kiniger
Affiliation:
Lehrstuhl für Optimale Steuerung, Technische Universität München, Fakultät für Mathematik, Boltzmannstraße 3, 85748 Garching b. München, Germany.. kiniger@ma.tum.de; vexler@ma.tum.de
Boris Vexler
Affiliation:
Lehrstuhl für Optimale Steuerung, Technische Universität München, Fakultät für Mathematik, Boltzmannstraße 3, 85748 Garching b. München, Germany.. kiniger@ma.tum.de; vexler@ma.tum.de
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Abstract

In this paper we consider a model shape optimization problem. The state variable solvesan elliptic equation on a domain with one part of the boundary described as the graph of acontrol function. We prove higher regularity of the control and develop a priorierror analysis for the finite element discretization of the shape optimizationproblem under consideration. The derived a priori error estimates areillustrated on two numerical examples.

Keywords

Shape optimizationexistence and convergence of approximate solutionserror estimatesfinite elements
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 6 , November 2013 , pp. 1733 - 1763
Copyright
© EDP Sciences, SMAI 2013

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