Geodesic
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

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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
Keywords: shape optimization, existence and convergence of approximate solutions, error estimates, finite elements 
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     author = {Kiniger, Bernhard and Vexler, Boris},
     title = {\protect\emph{A priori }error estimates for finite element discretizations of a shape optimization problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1733--1763},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {6},
     year = {2013},
     doi = {10.1051/m2an/2013086},
     zbl = {1283.49051},
     language = {en},
     url = {http://geodesic.mathdoc.fr/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

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