A semi-smooth Newton method for control constrained boundary optimal control of the Navier-Stokes equations

被引：51
作者：
de los Reyes, JC
Kunisch, K [1 ]
机构：
[1] Graz Univ, Inst Math & Sci Comp, A-8010 Graz, Austria
[2] EPN Quito, Dept Math, Quito, Ecuador
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2005年 / 62卷 / 07期
关键词：
optimal boundary control with control constraints; Navier-Stokes equations; semi-smooth Newton methods;
D O I：
10.1016/j.na.2005.04.035
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study optimal control of the Navier-Stokes equations when the control acts as a pointwise constrained boundary condition of Dirichlet type. The problem is analyzed in the control space H-00(1/2) the optimality system and second order sufficient optimality conditions are derived. For the numerical solution we apply a semi-smooth Newton method to a regularized version of the original problem and show convergence properties of the method and of the regularized solutions towards the original one. (c) 2005 Elsevier Ltd. All rights reserved.
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收藏
页码：1289 / 1316
页数：28
相关论文
共 34 条
  • [1] Abergel F., 1990, THEOR COMP FLUID DYN, V1, P303, DOI [DOI 10.1007/BF00271794, 10.1007/bf00271794]
  • [2] [Anonymous], 2000, MATH ANAL NUMERICAL
  • [3] Primal-dual strategy for constrained optimal control problems
    Bergounioux, M
    Ito, K
    Kunisch, K
    [J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1999, 37 (04) : 1176 - 1194
  • [4] Bonnans F, 2000, PERTURBATION ANAL OP
  • [5] Constantin P., 1988, Chicago Lectures in Mathematics, DOI DOI 10.7208/CHICAGO/9780226764320.001.0001
  • [6] Dautray R., 2000, Mathematical Analysis and Numerical Methods for Science and Technology. Vol. 5: Evolution Problems I
  • [7] A comparison of algorithms for control constrained optimal control of the Burgers equation
    de los Reyes, JC
    Kunisch, K
    [J]. CALCOLO, 2004, 41 (04) : 203 - 225
  • [8] DELOSREYES JC, 2003, THESIS U GRAZ
  • [9] OPTIMAL CONTROLS OF NAVIER-STOKES EQUATIONS
    DESAI, M
    ITO, K
    [J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1994, 32 (05) : 1428 - 1446
  • [10] Fattorini, 1999, INFINITE DIMENSIONAL, V62
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