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OPTIMAL CONTROL OF A STATIONARY NAVIER-STOKES HEMIVARIATIONAL INEQUALITY WITH NUMERICAL APPROXIMATION
Journal article   Open access   Peer reviewed

OPTIMAL CONTROL OF A STATIONARY NAVIER-STOKES HEMIVARIATIONAL INEQUALITY WITH NUMERICAL APPROXIMATION

Wensi Wang, Xiaoliang Cheng and Weimin Han
Discrete and continuous dynamical systems. Series A, Vol.44(8), pp.2309-2326
08/2024
DOI: 10.3934/dcds.2024028
url
https://doi.org/10.3934/dcds.2024028View
Published (Version of record) Open Access

Abstract

. In this paper, we study an optimal control problem for a stationary Navier-Stokes hemivariational inequality with control constraints and its numerical approximation. The hemivariational inequality is the weak formulation of a stationary incompressible fluid flow problem, modeled by the NavierStokes equations subject to a nonleak boundary condition and a subdifferential condition of friction type. We investigate the stability of the solution of the hemivariational inequality with respect to perturbations in the density of external force and superpotential, and demonstrate the existence of a solution for the optimal control problem with the external force density as the control. Moreover, we consider the numerical solution of the optimal control problem and show its convergence. As an example and for definiteness, the numerical solution is defined through the finite element method.
Mathematics Physical Sciences Mathematics, Applied Science & Technology

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