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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Through numerical examples, we show the efficiency of the stabilization for the solutions of the control, state, and adjoint variables.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we analyze a projection-based variational multiscale (VMS) method for the optimal control problems governed by the convection-diffusion-reaction equations.
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Key Findings & Data:We derive the first-order optimality conditions by the \emph{optimize-then-discretize} method.
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Conclusion & Impact:Through numerical examples, we show the efficiency of the stabilization for the solutions of the control, state, and adjoint variables.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Convection-diffusion · optimal control · finite element
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.
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Cite This Article
ÇIBIK, A. B., YILMAZ, F. N. (2018). Variational multiscale method for the optimal control problems of convectio--diffusion-reaction equations. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 1, 164–180. https://ajindex.com/articles/723141