| Optimal control problems have been widely applied in aerospace,environmental engineering, energy development, biological engineer-ing research. It is also extensively used in real life, such as, air pol-lution control, temperature control and population control and so on. From the perspective of mathematical analysis, the optimal con-trol problem can be converted into extreme-value problem. As a re-sult, researches of the numerical method of optimal control prob-lem have caused many scholars's attention. At present, numerical methods mainly include the finite element method, the finite volume element method(FVEM), the finite difference method, the spectral method and so on. Since the finite volume element method has the advantage of keeping the quantity of local conservation, researches of the finite volume element method cause the attention of scholars. In this paper, we study Fourier finite volume element method for two classes of optimal control problems governed by elliptic partial dif-ferential equations (PDEs) on the annular domain, both distributed control and the Dirichlet boundary control are given.In this paper, we consider two classes of optimal control problems governed by elliptic PDEs on an annular domain. In two problems,both a distributed control and a Dirichlet boundary control occur.Firstly, we obtain the optimality systems of such optimal control problems by the Lagrange multiplier method, and then discrete the optimality systems, which consist of state equation, adjoint equation and the optimality conditions. Secondly, we propose the Fourier fi-nite volume element method. In our proposed method, the Fourier discretization is utilized in the azimuthal direction while finite volume element approximation is used in the radial direction. We consider the Fourier finite volume element method to approximation the op-timality systems. Finally, Some numerical examples are presented to illustrate the accuracy and efficiency of our method. |
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