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.
Keywords: shape optimization, existence and convergence of approximate solutions, error estimates, finite elements
@article{M2AN_2013__47_6_1733_0,
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},
year = {2013},
publisher = {EDP Sciences},
volume = {47},
number = {6},
doi = {10.1051/m2an/2013086},
zbl = {1283.49051},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2013086/}
}
TY - JOUR AU - Kiniger, Bernhard AU - Vexler, Boris TI - A priori error estimates for finite element discretizations of a shape optimization problem JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 1733 EP - 1763 VL - 47 IS - 6 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2013086/ DO - 10.1051/m2an/2013086 LA - en ID - M2AN_2013__47_6_1733_0 ER -
%0 Journal Article %A Kiniger, Bernhard %A Vexler, Boris %T A priori error estimates for finite element discretizations of a shape optimization problem %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 1733-1763 %V 47 %N 6 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2013086/ %R 10.1051/m2an/2013086 %G en %F 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 , Tome 47 (2013) no. 6, pp. 1733-1763. doi: 10.1051/m2an/2013086
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