SPACE-TIME SPECTRAL METHODS FOR A FOURTH-ORDER PARABOLIC OPTIMAL CONTROL PROBLEM IN THREE CONTROL CONSTRAINT CASES

被引：0
|
作者：
Tao, Zhen-Zhen [1 ]
Sun, Bing [2 ,3 ]
机构：
[1] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454003, Henan, Peoples R China
[2] Beijing Inst Technol, Sch Math & Stat, Beijing 102488, Peoples R China
[3] Beijing Inst Technol, MIIT Key Lab MTCIS, Beijing 102488, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2023年 / 28卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Spectral approximation; a priori error; parabolic optimization problem; fourth-order; optimality conditions; FINITE-ELEMENT DISCRETIZATION; GALERKIN METHOD; STATE; APPROXIMATION; EQUATION;
D O I：
10.3934/dcdsb.2022080
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we are concerned with the space-time spectral discretization of an optimal control problem governed by a fourth-order parabolic partial differential equations (PDEs) in three control constraint cases. The dual Petrov-Galerkin spectral method in time and the spectral method in space are adopted to discrete the continuous system. By means of the obtained optimality condition for the continuous system and that of its spectral discrete system, we establish a priori error estimate for the spectral approximation in details. Four numerical examples are, subsequently, executed to confirm the theoretical results. The experiment results show the high efficiency and a good precision of the space-time spectral method for this kind of problems.
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页码：359 / 384
页数：26
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