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

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