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Yapay Zeka Hızlı Bakış & Çıkarımlar
AI Insight⚡ TL;DR(1 Cümlede Hızlı Çıkarım)
Through numerical examples, we show the efficiency of the stabilization for the solutions of the control, state, and adjoint variables.
📌 3 Maddede Bu Makale
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Amaç & Hipotez: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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Temel Bulgular & Veri:We derive the first-order optimality conditions by the \emph{optimize-then-discretize} method.
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Sonuç & Katkı:Through numerical examples, we show the efficiency of the stabilization for the solutions of the control, state, and adjoint variables.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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.
Anahtar kelimeler
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Bu Makaleye Atıf Yap
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