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.
@article{M2AN_2013__47_6_1733_0,
author = {Kiniger, Bernhard and Vexler, Boris},
title = {A priori error estimates for finite element discretizations of a shape optimization problem},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {47},
year = {2013},
pages = {1733-1763},
doi = {10.1051/m2an/2013086},
zbl = {1283.49051},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2013__47_6_1733_0}
}
Kiniger, Bernhard; Vexler, Boris. A priori error estimates for finite element discretizations of a shape optimization problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 47 (2013) pp. 1733-1763. doi : 10.1051/m2an/2013086. http://gdmltest.u-ga.fr/item/M2AN_2013__47_6_1733_0/
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