Volume 37, Number 5, September-October 2003
|Page(s)||833 - 850|
|Published online||15 November 2003|
Singular perturbation for the Dirichlet boundary control of elliptic problems
Mathématiques pour l'Industrie et la Physique,
Université Paul Sabatier, 31062 Toulouse Cedex 04,
2 LAMSIN, École Nationale d'Ingénieurs de Tunis, BP 37, 1002 Tunis-Belvédère, Tunisie. email@example.com.
3 LAMSIN, École Nationale d'Ingénieurs de Tunis, BP 37, 1002 Tunis-Belvédère, Tunisie. firstname.lastname@example.org.
Revised: 21 May 2003
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.
Mathematics Subject Classification: 49N05 / 49N10 / 34D15
Key words: Boundary control problems / non-smooth Dirichlet condition / Robin penalization / singularly perturbed problem.
© EDP Sciences, SMAI, 2003
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