A priori error estimates for finite element discretizations of a shape optimization problem
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 6, pp. 1733-1763.

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

DOI : 10.1051/m2an/2013086
Classification : 49Q10, 49M25, 65M15, 65M60
Mots clés : shape optimization, existence and convergence of approximate solutions, error estimates, finite elements
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     title = {\protect\emph{A priori }error estimates for finite element discretizations of a shape optimization problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
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     publisher = {EDP-Sciences},
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     url = {http://www.numdam.org/articles/10.1051/m2an/2013086/}
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Kiniger, Bernhard; Vexler, Boris. A priori error estimates for finite element discretizations of a shape optimization problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 6, pp. 1733-1763. doi : 10.1051/m2an/2013086. http://www.numdam.org/articles/10.1051/m2an/2013086/

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