A posteriori error estimates of hp spectral element methods for integral state constrained elliptic optimal control problems

被引：5
|
作者：
Chen, Yanping [1 ]
Zhang, Jinling [2 ]
Huang, Yunqing [3 ]
Xu, Yeqing [1 ]
机构：
[1] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China
[2] Xiangtan Univ, Sch Math & Comp Sci, Xiangtan 411105, Peoples R China
[3] Xiangtan Univ, Sch Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Peoples R China
来源：
APPLIED NUMERICAL MATHEMATICS | 2019年 / 144卷
基金：
中国国家自然科学基金;
关键词：
Elliptic equations; Optimal control; Integral state constraint; hp spectral element methods; A posteriori error estimates; APPROXIMATION; VERSION;
D O I：
10.1016/j.apnum.2019.05.015
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate the hp spectral element approximation for optimal control problem governed by elliptic equation with an integral constraint for state. We first present the optimality conditions of the continuous and discretized control problems, respectively. Then, hp a posteriori error estimates are obtained for the coupled state and control approximation. In the end, we use a simple and yet efficient projection algorithm to carry out ample numerical experiments which confirm our analytical results. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：42 / 58
页数：17
相关论文
共 50 条
  • [1] A Posteriori Error Estimates for hp Spectral Element Approximation of Elliptic Control Problems with Integral Control and State Constraints
    Zhang, Jinling
    Chen, Yanping
    Null, Yunqing Huang
    Huang, Fenglin
    [J]. ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2022, 14 (02) : 469 - 493
  • [2] A posteriori error estimates of hp spectral element method for parabolic optimal control problems
    Lu, Zuliang
    Cai, Fei
    Xu, Ruixiang
    Hou, Chunjuan
    Wu, Xiankui
    Yang, Yin
    [J]. AIMS MATHEMATICS, 2022, 7 (04): : 5220 - 5240
  • [3] A posteriori error estimates of hp spectral element methods for optimal control problems with L2-norm state constraint
    Lin, Xiuxiu
    Chen, Yanping
    Huang, Yunqing
    [J]. NUMERICAL ALGORITHMS, 2020, 83 (03) : 1145 - 1169
  • [4] A posteriori error estimates of hp spectral element methods for optimal control problems with L2-norm state constraint
    Xiuxiu Lin
    Yanping Chen
    Yunqing Huang
    [J]. Numerical Algorithms, 2020, 83 : 1145 - 1169
  • [5] A priori and a posteriori error analysis of hp spectral element discretization for optimal control problems with elliptic equations
    Lin, Xiuxiu
    Chen, Yanping
    Huang, Yunqing
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2023, 423
  • [6] A PRIORI AND POSTERIORI ERROR ESTIMATES OF LEGENDRE GALERKIN SPECTRAL METHODS FOR GENERAL ELLIPTIC OPTIMAL CONTROL PROBLEMS
    Lu, Zuliang
    Huang, Fei
    Lin, Li
    Cai, Fei
    Yang, Yin
    [J]. JOURNAL OF MATHEMATICAL INEQUALITIES, 2020, 14 (04): : 989 - 1006
  • [7] The Constants in A Posteriori Error Indicator for State-Constrained Optimal Control Problems with Spectral Methods
    Zhou, Jianwei
    [J]. ABSTRACT AND APPLIED ANALYSIS, 2014,
  • [8] A posteriori error estimates for hp finite element solutions of convex optimal control problems
    Chen, Yanping
    Lin, Yijie
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (12) : 3435 - 3454
  • [9] New a posteriori error estimates for hp version of finite element methods of nonlinear parabolic optimal control problems
    Lu, Zuliang
    Liu, Hongyan
    Hou, Chunjuan
    Cao, Longzhou
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016, : 1 - 17
  • [10] New a posteriori error estimates for hp version of finite element methods of nonlinear parabolic optimal control problems
    Zuliang Lu
    Hongyan Liu
    Chunjuan Hou
    Longzhou Cao
    [J]. Journal of Inequalities and Applications, 2016
12345