A posteriori error estimates of hp spectral element method for parabolic optimal control problems

被引：0
|
作者：
Lu, Zuliang [1 ,2 ]
Cai, Fei [3 ]
Xu, Ruixiang [3 ]
Hou, Chunjuan [4 ]
Wu, Xiankui [3 ]
Yang, Yin [5 ]
机构：
[1] Chongqing Three Gorges Univ, Key Lab Nonlinear Sci & Syst Struct, Key Lab Intelligent Informat Proc & Control, Chongqing 404000, Peoples R China
[2] Tianjin Univ Finance & Econ, Res Ctr Math & Econ, Tianjin 300222, Peoples R China
[3] Chongqing Three Gorges Univ, Key Lab Nonlinear Sci & Syst Struct, Chongqing 404000, Peoples R China
[4] Guangzhou Huashang Coll, Guangzhou 511300, Peoples R China
[5] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China
来源：
AIMS MATHEMATICS | 2022年 / 7卷 / 04期
基金：
美国国家科学基金会; 中国博士后科学基金;
关键词：
parabolic optimal control problems; hp spectral element method; a posteriori error estimates; MIXED FINITE-ELEMENT; NONSMOOTH FUNCTIONS; APPROXIMATION; SUPERCONVERGENCE; INTERPOLATION;
D O I：
10.3934/math.2022291
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate the spectral element approximation for the optimal control problem of parabolic equation, and present a hp spectral element approximation scheme for the parabolic optimal control problem. For improve the accuracy of the algorithm and construct an adaptive finite element approximation. Under the Scott-Zhang type quasi-interpolation operator, a L-2(H-1) - L-2(L-2) posteriori error estimates of the hp spectral element approximated solutions for both the state variables and the control variable are obtained. Adopting two auxiliary equations and stability results, a L-2(L-2)-L-2(L-2) posteriori error estimates are derived for the hp spectral element approximation of optimal parabolic control problem.
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页码：5220 / 5240
页数：21
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