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


Hacat G., Yılmaz F. N., Çıbık A. B., Kaya Merdan S.

Applied Mathematics and Computation, vol.430, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 430
  • Publication Date: 2022
  • Doi Number: 10.1016/j.amc.2022.127240
  • Journal Name: Applied Mathematics and Computation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, Public Affairs Index, zbMATH, Civil Engineering Abstracts
  • Keywords: Finite element method, Navier-Stokes equations, Optimal control, Curvature stabilization, VELOCITY TRACKING PROBLEM, CONSTRAINED OPTIMAL-CONTROL, A-PRIORI, FLOWS, APPROXIMATION
  • Middle East Technical University Affiliated: Yes

Abstract

© 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.