Fourier Finite Volume Element Method for Two Classes of Optimal Control Problems Governed by Elliptic PDEs on Complex Connected Domain. (11th March 2020)

• Record Type: Journal Article
• Authors: Lin, Xiuxiu; Su, Mengya; Zhang, Zhiyue
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 4(2020)
• Page Start: 379
• Page End: 412
• Publication Date: 2020-03-11
• Subjects: Fourier finite volume element method -- optimal control problems -- elliptic equation -- Dirichlet boundary control -- distributed control; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1658602
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this article, Fourier finite volume element method is provided to solve two classes of optimal control problems governed by elliptic PDEs. In two classes of problems, both distributed control and Dirichlet boundary control are given. We obtain the optimality systems of optimal control problems by the Lagrange multiplier method. Using the polar coordinates, the Fourier discretization is used in the azimuthal direction while the finite volume element approximation is used in the radial direction. In our proposed numerical method, the trial and test function spaces are carefully chosen to get accurate approximation. We use the Fourier finite volume method to approximate the control problems, the two-dimensional optimal control problem can be reduced to a one-dimensional problem. We not only observe that the convergent order of distributed control is second order, but also the convergent order of the Dirichlet boundary control is second order. Some numerical experiments are presented to illustrate accuracy and efficiency of our method.