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Turkish Journal of Mathematics

DOI

10.3906/mat-1606-111

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.

First Page

164

Last Page

180

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