Space-time spectral methods for a fourth-order parabolic optimal control problem in three control constraint cases-Reference-Cited by-同舟云学术

Space-time spectral methods for a fourth-order parabolic optimal control problem in three control constraint cases

Published:2023 Issue:1 Volume:28 Page:359
ISSN:1531-3492
Container-title:Discrete and Continuous Dynamical Systems - B
language:
Short-container-title:DCDS-B

Author:

Tao Zhen-Zhen¹,Sun Bing²³

Affiliation:

1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454003, China

2. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, China

3. MIIT Key Laboratory of MTCIS, Beijing Institute of Technology, Beijing 102488, China

Abstract

<p style='text-indent:20px;'>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.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics

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