A priori error estimates for finite element discretizations of a shape optimization problem
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 6, p. 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 : https://doi.org/10.1051/m2an/2013086
Classification:  49Q10,  49M25,  65M15,  65M60
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 = {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},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {6},
     year = {2013},
     pages = {1733-1763},
     doi = {10.1051/m2an/2013086},
     zbl = {1283.49051},
     language = {en},
     url = {http://www.numdam.org/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, Volume 47 (2013) no. 6, pp. 1733-1763. doi : 10.1051/m2an/2013086. http://www.numdam.org/item/M2AN_2013__47_6_1733_0/

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