- Turkish Journal of Mathematics
- Vol: 42 Issue: 1
- Variational multiscale method for the optimal control problems of convectio--diffusion-reaction equa...
Variational multiscale method for the optimal control problems of convectio--diffusion-reaction equations
Authors : Aytekin Bayram Çibik, Fikriye Nuray Yilmaz
Pages : 164-180
View : 8 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : Convection-diffusion, optimal control, finite element, VMS