A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem

被引：2
|
作者：
Li, Lin [1 ]
Lu, Zuliang [1 ,2 ,3 ]
Zhang, Wei [4 ]
Huang, Fei [1 ]
Yang, Yin [5 ,6 ]
机构：
[1] Chongqing Three Gorges Univ, Key Lab Nonlinear Sci & Syst Struct, Chongqing, Peoples R China
[2] Chongqing Three Gorges Univ, Key Lab Intelligent Informat Proc & Control, Chongqing, Peoples R China
[3] Tianjin Univ Finance & Econ, Res Ctr Math & Econ, Tianjin, Peoples R China
[4] Chongqing Three Gorges Univ, Chongqing Municipal Inst Higher Educ, Key Lab Intelligent Informat Proc & Control, Chongqing, Peoples R China
[5] Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan, Peoples R China
[6] Xiangtan Univ, Minist Educ, Key Lab Intelligent Comp & Informat Proc, Xiangtan, Peoples R China
来源：
JOURNAL OF INEQUALITIES AND APPLICATIONS | 2018年
基金：
美国国家科学基金会; 中国博士后科学基金;
关键词：
Optimal control problem; Nonlinear parabolic equations; Variational discretization; Spectral method; A posteriori error estimates; FINITE-ELEMENT METHODS; ELLIPTIC-EQUATIONS; APPROXIMATION;
D O I：
10.1186/s13660-018-1729-4
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 approximation of optimal control problem governed by nonlinear parabolic equations. A spectral approximation scheme for the nonlinear parabolic optimal control problem is presented. We construct a fully discrete spectral approximation scheme by using the backward Euler scheme in time. Moreover, by using an orthogonal projection operator, we obtain L-2(H-1)-L-2 (L-2) a posteriori error estimates of the approximation solutions for both the state and the control. Finally, by introducing two auxiliary equations, we also obtain L-2(L-2)-L-2(L-2) a posteriori error estimates of the approximation solutions for both the state and the control.
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页数：23
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