A Fourier–Legendre spectral element method in polar coordinates

• Published in: Journal of computational physics Vol. 231; no. 2; pp. 666 - 675
• Main Authors: Qiu, Zhouhua, Zeng, Zhong, Mei, Huan, Li, Liang, Yao, Liping, Zhang, Liangqi
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 2012; Elsevier
• Subjects: Computation; Computational techniques; Dirichlet problem; Exact sciences and technology; Galerkin methods; Legendre polynomials; Legendre-Gauss–Lobatto; Legendre–Gauss–Radau; Mathematical analysis; Mathematical methods in physics; Physics; Poisson-type equation; Polar coordinates; Poles; Singularities; Spectral element method; Spectral element method; Poisson-type equation; Legendre polynomials; Legendre–Gauss–Radau; Polar coordinates; Legendre-Gauss–Lobatto; Neumann problem; Singularity; Spectral method; Polar coordinate; Boundary conditions; Poisson equation; Legendre-Gauss-Radau; Calculation methods; Legendre-Gauss-Lobatto; Calculation
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2011.10.003

In this paper, a new Fourier–Legendre spectral element method based on the Galerkin formulation is proposed to solve the Poisson-type equations in polar coordinates. The 1/ r singularity at r = 0 is avoided by using Gauss–Radau type quadrature points. In order to break the time-step restriction in the time-dependent problems, the clustering of collocation points near the pole is prevented through the technique of domain decomposition in the radial direction. A number of Poisson-type equations subject to the Dirichlet or Neumann boundary condition are computed and compared with the results in literature, which reveals a desirable result.