Fourier Finite Volume Element Method For Dirichlet Boundary Control Problems Governed By Elliptic PDEs On An Annular Domain

Since optimal control problems as well as their computational methods are very important in engineering technology and application, they both have drawn wide public attention. Those methods are widely used in various areas, such as engineer-ing, petro-chemical, aerospace, management and biomedical sciences. In mathemat-ics, an optimal control problem can be converted into an extremum problem. In this thesis, we introduce optimal control problems object to certain partial differential equations. Using the Lagrange multiplier method, we obtain the optimality systems of such control problem, and then derive its discrete form as well.In this thesis, we study optimal control problem governed by an elliptic partial differential equation with Dirichlet boundary conditions. We propose a Fourier finite volume element method based on Galerkin variational formulation for the Dirichlet boundary elliptic equation on an annular domain. We apply the Fourier expansion in the azimuthal direction and use the finite volume element method in the radial direction respectively. Finally, we report some preliminary numerical results, indicating the feasibility of the method.