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, cilt.430, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 430
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1016/j.amc.2022.127240
  • Dergi Adı: Applied Mathematics and Computation
  • Derginin Tarandığı İndeksler: 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
  • Anahtar Kelimeler: Finite element method, Navier-Stokes equations, Optimal control, Curvature stabilization, VELOCITY TRACKING PROBLEM, CONSTRAINED OPTIMAL-CONTROL, A-PRIORI, FLOWS, APPROXIMATION
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

© 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.