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Article

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

School of Mathematics and Statistics, Shandong Normal University, Jinan 250000, China
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Author to whom correspondence should be addressed.
Academic Editors: Ravi P. Agarwal and Maria Alessandra Ragusa
Received: 5 April 2021 / Revised: 24 May 2021 / Accepted: 30 May 2021 / Published: 5 June 2021
(This article belongs to the Special Issue Nonlinear Dynamics and Analysis)
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. View Full-Text
Keywords: optimal control; convection dominated diffusion equation; SUPG stabilized VEM; a priori error estimate optimal control; convection dominated diffusion equation; SUPG stabilized VEM; a priori error estimate
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MDPI and ACS Style

Wang, Q.; Zhou, Z. SUPG-Stabilized Virtual Element Method for Optimal Control Problem Governed by a Convection Dominated Diffusion Equation. Entropy 2021, 23, 723. https://0-doi-org.brum.beds.ac.uk/10.3390/e23060723

AMA Style

Wang Q, Zhou Z. SUPG-Stabilized Virtual Element Method for Optimal Control Problem Governed by a Convection Dominated Diffusion Equation. Entropy. 2021; 23(6):723. https://0-doi-org.brum.beds.ac.uk/10.3390/e23060723

Chicago/Turabian Style

Wang, Qiming, and Zhaojie Zhou. 2021. "SUPG-Stabilized Virtual Element Method for Optimal Control Problem Governed by a Convection Dominated Diffusion Equation" Entropy 23, no. 6: 723. https://0-doi-org.brum.beds.ac.uk/10.3390/e23060723

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