Error analysis of spectral approximation for space-time fractional optimal control problems with control and state constraints

被引：7

作者：

Chen, Yanping ^{[1
]}

Lin, Xiuxiu ^{[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 411105, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2022年 / 413卷

基金：

中国国家自然科学基金;

关键词：

Optimal control problems; Space-time fractional diffusion equation; A priori error estimates; A posteriori error estimates; FINITE-ELEMENT APPROXIMATION; DIFFUSION EQUATION; FORMULATION;

D O I：

10.1016/j.cam.2022.114293

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, spectral discretization of optimal control problem governed by the space-time fractional diffusion equation with integral control and state constraints is investigated. The study of the optimality conditions is very important for analyzing the optimal control problem. Introducing the auxiliary equations and some important operators are to obtain a priori error estimates of spectral approximation for state, adjoint state and control variable rigorously. Additionally, reliable a posteriori error estimates are also proved for the optimal control problem carefully. The analysis results indicate that the errors decay exponentially when the data is smooth. (c) 2022 Elsevier B.V. All rights reserved.

引用

页数：15

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