A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem

In this paper, we investigate the spectral approximation of optimal control problem governed by nonlinear parabolic equations. A spectral approximation scheme for the nonlinear parabolic optimal control problem is presented. We construct a fully discrete spectral approximation scheme by using the ba...

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Detalles Bibliográficos
Autores principales: Li, Lin, Lu, Zuliang, Zhang, Wei, Huang, Fei, Yang, Yin
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6008391/
https://www.ncbi.nlm.nih.gov/pubmed/30137735
http://dx.doi.org/10.1186/s13660-018-1729-4
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author Li, Lin
Lu, Zuliang
Zhang, Wei
Huang, Fei
Yang, Yin
author_facet Li, Lin
Lu, Zuliang
Zhang, Wei
Huang, Fei
Yang, Yin
author_sort Li, Lin
collection PubMed
description In this paper, we investigate the spectral approximation of optimal control problem governed by nonlinear parabolic equations. A spectral approximation scheme for the nonlinear parabolic optimal control problem is presented. We construct a fully discrete spectral approximation scheme by using the backward Euler scheme in time. Moreover, by using an orthogonal projection operator, we obtain [Formula: see text] a posteriori error estimates of the approximation solutions for both the state and the control. Finally, by introducing two auxiliary equations, we also obtain [Formula: see text] a posteriori error estimates of the approximation solutions for both the state and the control.
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spelling pubmed-60083912018-07-04 A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem Li, Lin Lu, Zuliang Zhang, Wei Huang, Fei Yang, Yin J Inequal Appl Research In this paper, we investigate the spectral approximation of optimal control problem governed by nonlinear parabolic equations. A spectral approximation scheme for the nonlinear parabolic optimal control problem is presented. We construct a fully discrete spectral approximation scheme by using the backward Euler scheme in time. Moreover, by using an orthogonal projection operator, we obtain [Formula: see text] a posteriori error estimates of the approximation solutions for both the state and the control. Finally, by introducing two auxiliary equations, we also obtain [Formula: see text] a posteriori error estimates of the approximation solutions for both the state and the control. Springer International Publishing 2018-06-19 2018 /pmc/articles/PMC6008391/ /pubmed/30137735 http://dx.doi.org/10.1186/s13660-018-1729-4 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Li, Lin
Lu, Zuliang
Zhang, Wei
Huang, Fei
Yang, Yin
A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem
title A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem
title_full A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem
title_fullStr A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem
title_full_unstemmed A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem
title_short A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem
title_sort posteriori error estimates of spectral method for nonlinear parabolic optimal control problem
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6008391/
https://www.ncbi.nlm.nih.gov/pubmed/30137735
http://dx.doi.org/10.1186/s13660-018-1729-4
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