Superconvergence of semidiscrete finite element methods for bilinear parabolic optimal control problems

In this paper, a semidiscrete finite element method for solving bilinear parabolic optimal control problems is considered. Firstly, we present a finite element approximation of the model problem. Secondly, we bring in some important intermediate variables and their error estimates. Thirdly, we deriv...

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Detalles Bibliográficos
Autores principales: Tang, Yuelong, Hua, Yuchun
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5355540/
https://www.ncbi.nlm.nih.gov/pubmed/28367051
http://dx.doi.org/10.1186/s13660-017-1334-y
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author Tang, Yuelong
Hua, Yuchun
author_facet Tang, Yuelong
Hua, Yuchun
author_sort Tang, Yuelong
collection PubMed
description In this paper, a semidiscrete finite element method for solving bilinear parabolic optimal control problems is considered. Firstly, we present a finite element approximation of the model problem. Secondly, we bring in some important intermediate variables and their error estimates. Thirdly, we derive a priori error estimates of the approximation scheme. Finally, we obtain the superconvergence between the semidiscrete finite element solutions and projections of the exact solutions. A numerical example is presented to verify our theoretical results.
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spelling pubmed-53555402017-03-30 Superconvergence of semidiscrete finite element methods for bilinear parabolic optimal control problems Tang, Yuelong Hua, Yuchun J Inequal Appl Research In this paper, a semidiscrete finite element method for solving bilinear parabolic optimal control problems is considered. Firstly, we present a finite element approximation of the model problem. Secondly, we bring in some important intermediate variables and their error estimates. Thirdly, we derive a priori error estimates of the approximation scheme. Finally, we obtain the superconvergence between the semidiscrete finite element solutions and projections of the exact solutions. A numerical example is presented to verify our theoretical results. Springer International Publishing 2017-03-16 2017 /pmc/articles/PMC5355540/ /pubmed/28367051 http://dx.doi.org/10.1186/s13660-017-1334-y Text en © The Author(s) 2017 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
Tang, Yuelong
Hua, Yuchun
Superconvergence of semidiscrete finite element methods for bilinear parabolic optimal control problems
title Superconvergence of semidiscrete finite element methods for bilinear parabolic optimal control problems
title_full Superconvergence of semidiscrete finite element methods for bilinear parabolic optimal control problems
title_fullStr Superconvergence of semidiscrete finite element methods for bilinear parabolic optimal control problems
title_full_unstemmed Superconvergence of semidiscrete finite element methods for bilinear parabolic optimal control problems
title_short Superconvergence of semidiscrete finite element methods for bilinear parabolic optimal control problems
title_sort superconvergence of semidiscrete finite element methods for bilinear parabolic optimal control problems
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5355540/
https://www.ncbi.nlm.nih.gov/pubmed/28367051
http://dx.doi.org/10.1186/s13660-017-1334-y
work_keys_str_mv AT tangyuelong superconvergenceofsemidiscretefiniteelementmethodsforbilinearparabolicoptimalcontrolproblems
AT huayuchun superconvergenceofsemidiscretefiniteelementmethodsforbilinearparabolicoptimalcontrolproblems

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