Spectral approximation for optimal control problems governed by first bi-harmonic equation

被引：1
|
作者：
Lin, Xiuxiu [1 ]
Chen, Yanping [1 ]
Huang, Yunqing [2 ]
机构：
[1] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Peoples R China
[2] Xiangtan Univ, Sch Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan, Peoples R China
来源：
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2023年 / 39卷 / 04期
基金：
中国国家自然科学基金;
关键词：
a priori error estimates; first bi-harmonic equation; L-2-norm state constraint; optimal control problem; spectral methods; INTEGRAL CONSTRAINT; 4TH-ORDER EQUATION; STOKES EQUATIONS; ERROR ANALYSIS; STATE; PDE;
D O I：
10.1002/num.22988
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We investigate in the article the L-2-norm state constrained control problem with first bi-harmonic equation. First, the optimality conditions of the control problem are derived carefully, and spectral discretization of the problem is established. Based on the property of projection operator, we establish a priori error analysis for control variable, state, and adjoint state variable. Furthermore, the efficient projected gradient algorithm is proposed, and the numerical results we obtained verify the analytical results that it can provide high order accuracy and fast convergence rate.
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页码：2808 / 2822
页数：15
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