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Variational multiscale method for the optimal control problems of convection--diffusion--reaction equations
Turkish Journal of Mathematics
In this paper, we analyze a projection-based variational multiscale method (VMS) for the optimal control problems governed by the convection-diffusionreaction equations. We derive the first order optimality conditions by using 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 the numerical examples, we show the efficiency ofdoi:10.3906/mat-1606-111 fatcat:hqrtin42lzhedcya6ag35p4u6q