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.
Mots clés : boundary control problems, non-smooth Dirichlet condition, Robin penalization, singularly perturbed problem
@article{M2AN_2003__37_5_833_0, author = {Belgacem, Faker Ben and Fekih, Henda El and Metoui, Hejer}, title = {Singular perturbation for the {Dirichlet} boundary control of elliptic problems}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {833--850}, publisher = {EDP-Sciences}, volume = {37}, number = {5}, year = {2003}, doi = {10.1051/m2an:2003057}, mrnumber = {2020866}, zbl = {1051.49012}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2003057/} }
TY - JOUR AU - Belgacem, Faker Ben AU - Fekih, Henda El AU - Metoui, Hejer TI - Singular perturbation for the Dirichlet boundary control of elliptic problems JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2003 SP - 833 EP - 850 VL - 37 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2003057/ DO - 10.1051/m2an:2003057 LA - en ID - M2AN_2003__37_5_833_0 ER -
%0 Journal Article %A Belgacem, Faker Ben %A Fekih, Henda El %A Metoui, Hejer %T Singular perturbation for the Dirichlet boundary control of elliptic problems %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 833-850 %V 37 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2003057/ %R 10.1051/m2an:2003057 %G en %F M2AN_2003__37_5_833_0
Belgacem, Faker Ben; Fekih, Henda El; Metoui, Hejer. Singular perturbation for the Dirichlet boundary control of elliptic problems. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 5, pp. 833-850. doi : 10.1051/m2an:2003057. http://www.numdam.org/articles/10.1051/m2an:2003057/
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