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

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  • Haçat, Gülnur
  • Yılmaz, Fikriye
  • Çıbık, Aytekin
  • Kaya, Songül

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.

Suggested Citation

  • Haçat, Gülnur & Yılmaz, Fikriye & Çıbık, Aytekin & Kaya, Songül, 2022. "Error estimates for the optimal control of Navier-Stokes equations using curvature based stabilization," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    • Handle: RePEc:eee:apmaco:v:430:y:2022:i:c:s0096300322003149
    DOI: 10.1016/j.amc.2022.127240
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    1. Yılmaz, Fikriye, 2016. "Semi-discrete a priori error analysis for the optimal control of the unsteady Navier–Stokes equations with variational multiscale stabilization," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 127-142.
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