Turkish Journal of Mathematics
Abstract
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 \emph{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.
DOI
10.3906/mat-1606-111
Keywords
Convection-diffusion, optimal control, finite element, VMS
First Page
164
Last Page
180
Recommended Citation
ÇIBIK, AYTEKİN BAYRAM and YILMAZ, FİKRİYE NURAY
(2018)
"Variational multiscale method for the optimal control problems of convectio--diffusion-reaction equations,"
Turkish Journal of Mathematics: Vol. 42:
No.
1, Article 15.
https://doi.org/10.3906/mat-1606-111
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss1/15
