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

Date

2022-10-01

Author

Hacat, Gülnur
Yılmaz, Fikriye Nuray
Çıbık, Aytekin Bayram
Kaya Merdan, Songül

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© 2022 Elsevier Inc.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.

Subject Keywords

Curvature stabilization, Finite element method, Navier-Stokes equations, Optimal control

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85130527794&origin=inward
https://hdl.handle.net/11511/97550

Journal

Applied Mathematics and Computation

DOI

https://doi.org/10.1016/j.amc.2022.127240

Collections

Department of Mathematics, Article

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Citation Formats

G. Hacat, F. N. Yılmaz, A. B. Çıbık, and S. Kaya Merdan, “Error estimates for the optimal control of Navier-Stokes equations using curvature based stabilization,” Applied Mathematics and Computation, vol. 430, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85130527794&origin=inward.