Error estimates for the optimal control of Navier-Stokes equations using curvature based stabilization

Gülnur Haçat, Fikriye Yılmaz, Aytekin Çıbık and Songül Kaya

Applied Mathematics and Computation, 2022, vol. 430, issue C

Abstract: This paper presents a family of implicit-explicit (IMEX) time stepping scheme for the optimal control problem of the unsteady Navier-Stokes equations (NSE). The main feature of this kind of optimal control problem is that stabilization terms are proportional to discrete curvature of the solutions. First and second order optimality conditions are used for optimality of the curvature based stabilized Navier-Stokes equations. Complete stability and error analyses of state, adjoint and control variables are presented. Numerical experiments verify theoretical findings and illustrate the improvement of approximate solutions enhancing the efficiency of numerical scheme.

Keywords: Finite element method; Navier-Stokes equations; Optimal control; Curvature stabilization (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:430:y:2022:i:c:s0096300322003149

DOI: 10.1016/j.amc.2022.127240

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