Finite element approximation and iterative method solution of elliptic control problem with constraints to gradient of state

被引：2
作者：
Dautov R. [1 ]
Lapin A. [1 ]
机构：
[1] Kazan Federal University, Kremlevskaya ul. 18, Kazan, Tatarstan
来源：
Lobachevskii Journal of Mathematics | 2015年 / 36卷 / 1期
关键词：
constrained saddle point problem; finite element method; iterative method; optimal control;
D O I：
10.1134/S1995080215010059
中图分类号：
学科分类号：
摘要：
An optimal control problem with distributed control in the right-hand side of Poisson equation is considered. Pointwise constraints on the gradient of state and control are imposed in this problem. The convergence of finite element approximation for this problem is proved. Discrete saddle point problem is constructed and preconditioned Uzawa-type iterative algorithm for its solution is investigated. © 2015, Pleiades Publishing, Ltd.
引用
收藏
页码：65 / 75
页数：10
相关论文
共 25 条
  • [1] Dautov R., Kadyrov R., Laitinen E., Lapin A., Pieska J., Toivonen V., Lobachevskii J.Math., 13, (2003)
  • [2] Laitinen E., Lapin A., Pieska J., J. Comp. Appl.Math., 154, (2003)
  • [3] Pieska J., Laitinen E., Lapin A., Domain Decomposition Methods in Science and Engineering, (2005)
  • [4] Bergounioux M., Haddou V., Hintermuller M., Kunisch K., SIAM J. Optim., 11, (2000)
  • [5] Bergounioux M., Kunisch K., Comput. Optim. Appl., 22, (2002)
  • [6] Troltzsch F., Pufert U., Weiser M., Comput. Optim. Appl., 39, (2008)
  • [7] Troltzsch F., Yousept I., Comput. Optim. Appl., 42, (2009)
  • [8] Hintermuller M., Hinze M., SIAM J. Numer. Anal., 47, (2009)
  • [9] Hinze M., Schiela A., Comput. Optim. Appl., 48, (2011)
  • [10] Casas E., Fernandez L., Appl. Math. Optimization., 27, (1993)
123