Analysis and discretization of an optimal control problem for the time-periodic MHD equations

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• 作者：Gunzburger ; Max ; Trenchea ; Catalin
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2005
• 出版时间：August 15, 2005
• 年：2005
• 卷：308
• 期：2
• 页码：440-466
• 全文大小：237 K

文摘

We consider the mathematical formulation and analysis of an optimal control problem associated with the tracking of the velocity and the magnetic field of a viscous, incompressible, electrically conducting fluid in a bounded two-dimensional domain through the adjustment of distributed controls. Existence of optimal solutions is proved and first-order necessary conditions for optimality are used to derive an optimality system of partial differential equations whose solutions provide optimal states and controls. Semidiscrete-in-time approximations are defined and their convergence to the exact optimal solutions is shown.