Singular perturbation for the Dirichlet boundary control of elliptic problems
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 37 (2003) no. 5, pp. 833-850.

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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.

DOI : 10.1051/m2an:2003057
Classification : 49N05, 49N10, 34D15
Mots-clés : boundary control problems, non-smooth Dirichlet condition, Robin penalization, singularly perturbed problem 
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     author = {Belgacem, Faker Ben and Fekih, Henda El and Metoui, Hejer},
     title = {Singular perturbation for the {Dirichlet} boundary control of elliptic problems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {833--850},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {5},
     year = {2003},
     doi = {10.1051/m2an:2003057},
     zbl = {1051.49012},
     mrnumber = {2020866},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2003057/}
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Belgacem, Faker Ben; Fekih, Henda El; Metoui, Hejer. Singular perturbation for the Dirichlet boundary control of elliptic problems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 37 (2003) no. 5, pp. 833-850. doi : 10.1051/m2an:2003057. https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2003057/

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