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existence and convergence of approximate solutions

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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A priori error estimates for finite elementdiscretizations of a shape optimization problem
Bernhard Kiniger, Boris Vexler
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 47 / Issue 6 / November 2013

Published online by Cambridge University Press:

07 October 2013, pp. 1733-1763

Print publication:

November 2013
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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.