Singular perturbation for the Dirichlet boundary control of elliptic problems

被引：16
作者：
Ben Belgacem, F [1 ]
El Fekih, H
Metoui, H
机构：
[1] Univ Toulouse 3, UMR 5640, F-31062 Toulouse 04, France
[2] Ecole Natl Ingn Tunis, LAMSIN, Tunis 1002, Tunisia
来源：
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2003年 / 37卷 / 05期
关键词：
boundary control problems; non-smooth Dirichlet condition; Robin penalization; singularly perturbed problem;
D O I：
10.1051/m2an:2003057
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 on to highlight the reliability of such an approach.
引用
收藏
页码：833 / 850
页数：18
相关论文
共 20 条
  • [1] [Anonymous], 1975, SOBOLEV SPACES
  • [2] Arada N, 2000, ASYMPTOTIC ANAL, V24, P343
  • [3] FINITE-ELEMENT METHOD WITH PENALTY
    BABUSKA, I
    [J]. MATHEMATICS OF COMPUTATION, 1973, 27 (122) : 221 - 228
  • [4] Ben Belgacem F, 2003, ASYMPTOTIC ANAL, V34, P121
  • [5] Augmented Lagrangian techniques for elliptic state constrained optimal control problems
    Bergounioux, M
    Kunisch, K
    [J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1997, 35 (05) : 1524 - 1543
  • [6] BOSSAVIT A, 1969, SEMINAIRE JL LIONS, V12
  • [7] Brezzi F., 2012, MIXED HYBRID FINITE, V15
  • [8] COLLIFRANZONE P, 1973, LECT NOTES COMPUTER, V3, P152
  • [9] COLLIFRANZONE P, 1973, B UNIONE MAT ITAL, V7, P229
  • [10] Costabel M, 1996, COMMUN PART DIFF EQ, V21, P1919
12