Semi-discrete a priori error analysis for the optimal control of the unsteady Navier-Stokes equations with variational multiscale stabilization

YILMAZ F. N.

APPLIED MATHEMATICS AND COMPUTATION, cilt.276, ss.127-142, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 276
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1016/j.amc.2015.11.092
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.127-142
  • Anahtar Kelimeler: Optimal control, Variational multiscale methods, Stabilized fem, Unsteady Navier-Stokes, Error estimate, FINITE-ELEMENT METHODS, APPROXIMATION
  • Gazi Üniversitesi Adresli: Evet

Özet

In this work, the optimal control problems of the unsteady Navier-Stokes equations with variational multiscale stabilization (VMS) are considered. At first, the first order continuous optimality conditions are obtained. Since the adjoint equation of the Navier-Stokes problem is a convection diffusion type system, then the same stabilization is applied to it. Semi discrete a priori error estimates are obtained for the state, adjoint state and control variables. Crank Nicholson time discretization is used to get the fully discrete scheme. Numerical examples verify the theoretical findings and show the efficiency of the stabilization for higher Reynolds number. (C) 2015 Elsevier Inc. All rights reserved.