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

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

2009-10-27

arxiv.org/abs/0910.5088v1

Mathematics

Numerical Analysis

30 pages, 5 figures

Scientific paper

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}.

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