A PRIORI AND POSTERIORI ERROR ESTIMATES OF LEGENDRE GALERKIN SPECTRAL METHODS FOR GENERAL ELLIPTIC OPTIMAL CONTROL PROBLEMS

被引：0

作者：

Lu, Zuliang ^{[1
,2
]}

Huang, Fei ^{[1
]}

Lin, Li ^{[3
]}

Cai, Fei ^{[1
]}

Yang, Yin ^{[4
]}

机构：

[1] Chongqing Three Gorges Univ, Key Lab Nonlinear Sci & Syst Struct, Chongqing 404000, Peoples R China

[2] Tianjin Univ Finance & Econ, Res Ctr Math & Econ, Tianjin 300222, Peoples R China

[3] Chongqing Univ Posts & Telecommun, Coll Comp Sci & Technol, Chongqing 400065, Peoples R China

[4] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

来源：

JOURNAL OF MATHEMATICAL INEQUALITIES | 2020年 / 14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：

General optimal control problems; Legendre Galerkin spectral method; a priori error estimate; a posteriori error estimates; FINITE-ELEMENT-METHOD; APPROXIMATION; 2ND-ORDER;

D O I：

10.7153/jmi-2020-14-65

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the Legendre Galerkin spectral method is applied to solve the constrained optimal control problems governed by general elliptic equations. Under some reasonable assumptions, by using the orthogonal projection operator, we derive a priori error estimates for the spectral approximation of optimal control problems. Then, we obtain a posteriori error estimates for both the state and the control approximation, where we use the L-2-norm for estimating the control approximation error, and the H-1-norm or L-2-norm for the state and co-state approximation error. Finally, some numerical experiments are presented to test our theoretical results.

引用

页码：989 / 1006

页数：18

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