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Journal of Scientific Computing

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01-12-2023

Adaptive Virtual Element Method for Optimal Control Problem Governed by Stokes Equations

Authors: Yanwei Li, Qiming Wang, Zhaojie Zhou

Published in: Journal of Scientific Computing | Issue 3/2023

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Abstract

In this paper, adaptive virtual element method (VEM) approximation of optimal control problem governed by Stokes equations with control constraints is discussed. The virtual element discrete scheme of the optimal control problem is constructed by polynomial projections and variational discretization of the control variable. Based on the a posteriori error estimates of VEM for Stokes equations and approximated error equivalence between the solutions of the optimal control problem and the solutions of the state and adjoint equations, we build up upper and lower bounds for the a posteriori error estimates of the optimal control problem. It proves that the a posteriori error indicator is reliable and efficient. The theoretical findings are illustrated by the numerical experiments.

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Title: Adaptive Virtual Element Method for Optimal Control Problem Governed by Stokes Equations
Authors: Yanwei Li
Qiming Wang
Zhaojie Zhou
Publication date: 01-12-2023
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 3/2023
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-023-02377-1

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