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.

引用

页数：23

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