# Singular perturbation for the Dirichlet boundary control of elliptic problems

Faker Ben Belgacem; Henda El Fekih; Hejer Metoui

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

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topBelgacem, 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 -

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