SUPG-Stabilized Virtual Element Method for Optimal Control Problem Governed by a Convection Dominated Diffusion Equation

In this paper, the streamline upwind/Petrov Galerkin (SUPG) stabilized virtual element method (VEM) for optimal control problem governed by a convection dominated diffusion equation is investigated. The virtual element discrete scheme is constructed based on the first-optimize-then-discretize strate...

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Autores principales: Wang, Qiming, Zhou, Zhaojie
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8230298/
https://www.ncbi.nlm.nih.gov/pubmed/34198952
http://dx.doi.org/10.3390/e23060723
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author Wang, Qiming
Zhou, Zhaojie
author_facet Wang, Qiming
Zhou, Zhaojie
author_sort Wang, Qiming
collection PubMed
description In this paper, the streamline upwind/Petrov Galerkin (SUPG) stabilized virtual element method (VEM) for optimal control problem governed by a convection dominated diffusion equation is investigated. The virtual element discrete scheme is constructed based on the first-optimize-then-discretize strategy and SUPG stabilized virtual element approximation of the state equation and adjoint state equation. An a priori error estimate is derived for both the state, adjoint state, and the control. Numerical experiments are carried out to illustrate the theoretical findings.
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spelling pubmed-82302982021-06-26 SUPG-Stabilized Virtual Element Method for Optimal Control Problem Governed by a Convection Dominated Diffusion Equation Wang, Qiming Zhou, Zhaojie Entropy (Basel) Article In this paper, the streamline upwind/Petrov Galerkin (SUPG) stabilized virtual element method (VEM) for optimal control problem governed by a convection dominated diffusion equation is investigated. The virtual element discrete scheme is constructed based on the first-optimize-then-discretize strategy and SUPG stabilized virtual element approximation of the state equation and adjoint state equation. An a priori error estimate is derived for both the state, adjoint state, and the control. Numerical experiments are carried out to illustrate the theoretical findings. MDPI 2021-06-05 /pmc/articles/PMC8230298/ /pubmed/34198952 http://dx.doi.org/10.3390/e23060723 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Wang, Qiming
Zhou, Zhaojie
SUPG-Stabilized Virtual Element Method for Optimal Control Problem Governed by a Convection Dominated Diffusion Equation
title SUPG-Stabilized Virtual Element Method for Optimal Control Problem Governed by a Convection Dominated Diffusion Equation
title_full SUPG-Stabilized Virtual Element Method for Optimal Control Problem Governed by a Convection Dominated Diffusion Equation
title_fullStr SUPG-Stabilized Virtual Element Method for Optimal Control Problem Governed by a Convection Dominated Diffusion Equation
title_full_unstemmed SUPG-Stabilized Virtual Element Method for Optimal Control Problem Governed by a Convection Dominated Diffusion Equation
title_short SUPG-Stabilized Virtual Element Method for Optimal Control Problem Governed by a Convection Dominated Diffusion Equation
title_sort supg-stabilized virtual element method for optimal control problem governed by a convection dominated diffusion equation
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8230298/
https://www.ncbi.nlm.nih.gov/pubmed/34198952
http://dx.doi.org/10.3390/e23060723
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AT zhouzhaojie supgstabilizedvirtualelementmethodforoptimalcontrolproblemgovernedbyaconvectiondominateddiffusionequation

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