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Zbl 1051.49012
Ben Belgacem, Faker; El Fekih, Henda; Metoui, Hejer
Singular perturbation for the Dirichlet boundary control of elliptic problems. (English)
[J] M2AN, Math. Model. Numer. Anal. 37, No. 5, 833-850 (2003). ISSN 0764-583X; ISSN 1290-3841/e

Summary: A current procedure that takes into account the Dirichlet boundary condition with nonsmooth 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 to highlight the reliability of such an approach.

MSC 2000:: *49K20 Optimal control problems with PDE (nec./ suff.)
35B25 Singular perturbations (PDE)
35J25 Second order elliptic equations, boundary value problems
35A35 Theoretical approximation to solutions of PDE
65M60 Finite numerical methods (IVP of PDE)

Keywords: boundary control problems; non-smooth Dirichlet boundary condition; Robin penalization; singularly perturbed problem; optimal control; regularity

Cited in: Zbl 1158.49002

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