A priori error estimates for finite element discretizations of a shape optimization problem

Bernhard Kiniger; Boris Vexler

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 6, page 1733-1763
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Kiniger, Bernhard, and 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 47.6 (2013): 1733-1763. <http://eudml.org/doc/273318>.

@article{Kiniger2013,
abstract = {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.},
author = {Kiniger, Bernhard, Vexler, Boris},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {shape optimization; existence and convergence of approximate solutions; error estimates; finite elements; approximate solutions},
language = {eng},
number = {6},
pages = {1733-1763},
publisher = {EDP-Sciences},
title = {A priori error estimates for finite element discretizations of a shape optimization problem},
url = {http://eudml.org/doc/273318},
volume = {47},
year = {2013},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 6
SP - 1733
EP - 1763
AB - 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.
LA - eng
KW - shape optimization; existence and convergence of approximate solutions; error estimates; finite elements; approximate solutions
UR - http://eudml.org/doc/273318
ER -

References

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