Journal article
OPTIMAL CONTROL OF A STATIONARY NAVIER-STOKES HEMIVARIATIONAL INEQUALITY WITH NUMERICAL APPROXIMATION
Discrete and continuous dynamical systems. Series A, Vol.44(8), pp.2309-2326
08/2024
DOI: 10.3934/dcds.2024028
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.
Details
- Title: Subtitle
- OPTIMAL CONTROL OF A STATIONARY NAVIER-STOKES HEMIVARIATIONAL INEQUALITY WITH NUMERICAL APPROXIMATION
- Creators
- Wensi Wang - Zhejiang UniversityXiaoliang Cheng - Zhejiang UniversityWeimin Han - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Discrete and continuous dynamical systems. Series A, Vol.44(8), pp.2309-2326
- DOI
- 10.3934/dcds.2024028
- ISSN
- 1078-0947
- eISSN
- 1553-5231
- Publisher
- Amer Inst Mathematical Sciences-Aims
- Number of pages
- 18
- Grant note
- 850737 / Simons Foundation Collaboration, USA Grants 823731-CONMECH / European Union; European Union (EU)
- Language
- English
- Electronic publication date
- 03/01/2024
- Date published
- 08/2024
- Academic Unit
- Mathematics
- Record Identifier
- 9984584907002771
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