Singular perturbation for the Dirichlet boundary control of elliptic problems

Faker Ben Belgacem; Henda El Fekih; Hejer Metoui

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • 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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Ben Belgacem, Faker, El Fekih, Henda, and Metoui, Hejer. "Singular perturbation for the Dirichlet boundary control of elliptic problems." ESAIM: Mathematical Modelling and Numerical Analysis 37.5 (2010): 833-850. <http://eudml.org/doc/194193>.

@article{BenBelgacem2010,
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 = {Ben Belgacem, Faker, El Fekih, Henda, Metoui, Hejer},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Boundary control problems; non-smooth Dirichlet condition; Robin penalization; singularly perturbed problem.; boundary control problems; non-smooth Dirichlet boundary condition; Robin penalization; singularly perturbed problem; optimal control; regularity},
language = {eng},
month = {3},
number = {5},
pages = {833-850},
publisher = {EDP Sciences},
title = {Singular perturbation for the Dirichlet boundary control of elliptic problems},
url = {http://eudml.org/doc/194193},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Ben Belgacem, Faker
AU - El Fekih, Henda
AU - Metoui, Hejer
TI - Singular perturbation for the Dirichlet boundary control of elliptic problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
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.; boundary control problems; non-smooth Dirichlet boundary condition; Robin penalization; singularly perturbed problem; optimal control; regularity
UR - http://eudml.org/doc/194193
ER -

References

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