# 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

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topBen 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 -

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