Adaptive Finite Element Approximation for a Constrained Optimal Control Problem via Multi-meshes

被引:0
作者
Liang Ge
Wenbin Liu
Danping Yang
机构
[1] Shandong University,Department of Mathematics
[2] University of Kent,KBS and IMS
[3] East China Normal University,Department of Mathematics
来源
Journal of Scientific Computing | 2009年 / 41卷
关键词
Optimal control problems; Adaptive finite element methods; A posteriori error estimates; Multi-meshes;
D O I
暂无
中图分类号
学科分类号
摘要
In this paper, we study adaptive finite element approximation schemes for a constrained optimal control problem. We derive the equivalent a posteriori error estimators for both the state and the control approximation, which particularly suit an adaptive multi-mesh finite element scheme. The error estimators are then implemented and tested with promising numerical results.
引用
收藏
相关论文
共 31 条
[1]  
Ainsworth M.(1997)A posteriori error estimators in finite element analysis Comput. Methods Appl. Mech. Eng. 142 1-88
[2]  
Oden J.T.(2008)Superconvergence analysis of finite element methods for optimal control problems of the stationary Benard type J. Comput. Math. 26 660-676
[3]  
Chang Y.Z.(2000)Adaptive finite element methods for optimal control of partial differential equations: basic concept SIAM J. Control Optim. 39 113-132
[4]  
Yang D.P.(2001)Analysis of inexact trust-region SQP algorithms SIAM J. Optim. 12 283-302
[5]  
Becker R.(1999)A trust region method for parabolic boundary control problems SIAM J. Optim. 9 1064-1091
[6]  
Kapp H.(2005)On multi-mesh JSC 24 321-341
[7]  
Rannacher R.(2002)-adaptive algorithm SIAM J. Control. Optim. 41 1321-1349
[8]  
Heinkenschloss K.(2005)Adaptive finite element approximation of elliptic optimal control Contemp. Math. 383 113-132
[9]  
Vicente L.N.(2009)Adaptive multi-meshes in finite element approximation of optimal control J. Comput. Math. 27 97-114
[10]  
Kelley C.T.(2001)A new finite element approximation of a state-constrained optimal control problem Adv. Comput. Math. 15 285-309