Variational multiscale method for the optimal control problems of convection-diffusion-reaction equations

ÇIBIK A. B., YILMAZ F. N.

TURKISH JOURNAL OF MATHEMATICS, cilt.42, sa.1, ss.164-180, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 1
  • Basım Tarihi: 2018
  • Doi Numarası: 10.3906/mat-1606-111
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.164-180
  • Anahtar Kelimeler: Convection-diffusion, optimal control, finite element, VMS, FINITE-ELEMENT METHODS, EDDY VISCOSITY
  • Gazi Üniversitesi Adresli: Evet

Özet

In this paper, we analyze a projection-based variational multiscale (VMS) method for the optimal control problems governed by the convection diffusion reaction equations. We derive the first-order optimality conditions by the optimize-then-discretize method. After expressing the discrete optimal control problem, we obtain the stability properties of state and adjoint variables. We also prove that the error in each variable is optimal. Through numerical examples, we show the efficiency of the stabilization for the solutions of the control, state, and adjoint variables.