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Singular perturbation for the Dirichlet boundary control of elliptic problems

Published online by Cambridge University Press:  15 November 2003

Faker Ben Belgacem ,
Henda El Fekih  and
Hejer Metoui
Faker Ben Belgacem
Affiliation:
Mathématiques pour l'Industrie et la Physique, UMR 5640, Université Paul Sabatier, 31062 Toulouse Cedex 04, France. belgacem@mip.ups-tlse.fr.
Henda El Fekih
Affiliation:
LAMSIN, École Nationale d'Ingénieurs de Tunis, BP 37, 1002 Tunis-Belvédère, Tunisie. henda.elfekih@enit.rnu.tn.
Hejer Metoui
Affiliation:
LAMSIN, École Nationale d'Ingénieurs de Tunis, BP 37, 1002 Tunis-Belvédère, Tunisie. hajer.metoui@enit.rnu.tn.
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Abstract

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

Keywords

Boundary control problemsnon-smooth Dirichlet conditionRobin penalizationsingularly perturbed problem.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 5 , September 2003 , pp. 833 - 850
Copyright
© EDP Sciences, SMAI, 2003

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