Singular perturbation for the Dirichlet boundary control of elliptic problems

Faker Ben Belgacem; Henda El Fekih; Hejer Metoui

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2003)

  • Volume: 37, Issue: 5, page 833-850
  • ISSN: 0764-583X

Abstract

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A current procedure that takes into account the Dirichlet boundary condition with non-smooth data is to change it into a Robin type condition by introducing a penalization term; a major effect of this procedure is an easy implementation of the boundary condition. In this work, we deal with an optimal control problem where the control variable is the Dirichlet data. We describe the Robin penalization, and we bound the gap between the penalized and the non-penalized boundary controls for the small penalization parameter. Some numerical results are reported on to highlight the reliability of such an approach.

How to cite

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Belgacem, Faker Ben, Fekih, Henda El, and Metoui, Hejer. "Singular perturbation for the Dirichlet boundary control of elliptic problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 37.5 (2003): 833-850. <http://eudml.org/doc/246001>.

@article{Belgacem2003,
abstract = {A current procedure that takes into account the Dirichlet boundary condition with non-smooth data is to change it into a Robin type condition by introducing a penalization term; a major effect of this procedure is an easy implementation of the boundary condition. In this work, we deal with an optimal control problem where the control variable is the Dirichlet data. We describe the Robin penalization, and we bound the gap between the penalized and the non-penalized boundary controls for the small penalization parameter. Some numerical results are reported on to highlight the reliability of such an approach.},
author = {Belgacem, Faker Ben, Fekih, Henda El, Metoui, Hejer},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {boundary control problems; non-smooth Dirichlet condition; Robin penalization; singularly perturbed problem; non-smooth Dirichlet boundary condition; optimal control; regularity},
language = {eng},
number = {5},
pages = {833-850},
publisher = {EDP-Sciences},
title = {Singular perturbation for the Dirichlet boundary control of elliptic problems},
url = {http://eudml.org/doc/246001},
volume = {37},
year = {2003},
}

TY - JOUR
AU - Belgacem, Faker Ben
AU - Fekih, Henda El
AU - Metoui, Hejer
TI - Singular perturbation for the Dirichlet boundary control of elliptic problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2003
PB - EDP-Sciences
VL - 37
IS - 5
SP - 833
EP - 850
AB - A current procedure that takes into account the Dirichlet boundary condition with non-smooth data is to change it into a Robin type condition by introducing a penalization term; a major effect of this procedure is an easy implementation of the boundary condition. In this work, we deal with an optimal control problem where the control variable is the Dirichlet data. We describe the Robin penalization, and we bound the gap between the penalized and the non-penalized boundary controls for the small penalization parameter. Some numerical results are reported on to highlight the reliability of such an approach.
LA - eng
KW - boundary control problems; non-smooth Dirichlet condition; Robin penalization; singularly perturbed problem; non-smooth Dirichlet boundary condition; optimal control; regularity
UR - http://eudml.org/doc/246001
ER -

References

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