A spectral method based on $(0,2)$ Jacobi polynomials. Application to Poisson problems in a sphere

Abstract

A new spectral method is built resorting to $(0,2)$ Jacobi polynomials. We describe the origin and the properties of these polynomials. This choice of polynomials is motivated by their orthogonality properties with the respect to the weight $r^2$ used in spherical geometry. New results about Jacobi-Gauss-Lobatto quadratures are proven, leading to a discrete Jacobi transform. Numerical tests for Poisson problems in a sphere are presented using the C++ library \textsc{lorene}.

30 pages, 5 figures

References in corpus (1)

• Numerical approach for high precision 3-D relativistic star models