A posteriori error estimates of hp spectral element method for parabolic optimal control problems-Reference-Cited by-同舟云学术

A posteriori error estimates of hp spectral element method for parabolic optimal control problems

Published:2022 Issue:4 Volume:7 Page:5220-5240
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Lu Zuliang¹²,Cai Fei³,Xu Ruixiang³,Hou Chunjuan⁴,Wu Xiankui³,Yang Yin⁵

Affiliation:

1. Key Laboratory for Nonlinear Science and System Structure, Key Laboratory of Intelligent Information Processing and Control, Chongqing Three Gorges University, Chongqing 404000, China

2. Research Center for Mathematics and Economics, Tianjin University of Finance and Economics, Tianjin 300222, China

3. Key Laboratory for Nonlinear Science and System Structure, Chongqing Three Gorges University, Chongqing 404000, China

4. Guangzhou Huashang College, Guangzhou 511300, China

5. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105 Hunan, China

Abstract

<abstract><p>In this paper, we investigate the spectral element approximation for the optimal control problem of parabolic equation, and present a hp spectral element approximation scheme for the parabolic optimal control problem. For improve the accuracy of the algorithm and construct an adaptive finite element approximation. Under the Scott-Zhang type quasi-interpolation operator, a $ L^2(H^1)-L^2(L^2) $ posteriori error estimates of the hp spectral element approximated solutions for both the state variables and the control variable are obtained. Adopting two auxiliary equations and stability results, a $ L^2(L^2)-L^2(L^2) $ posteriori error estimates are derived for the hp spectral element approximation of optimal parabolic control problem.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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