{
  "id": "0910.5088",
  "version": "v1",
  "published": "2009-10-27T11:19:20.000Z",
  "updated": "2009-10-27T11:19:20.000Z",
  "title": "A spectral method based on $(0,2)$ Jacobi polynomials. Application to Poisson problems in a sphere",
  "authors": [
    "Cornou Jean-Louis",
    "Bonazzola Silvano"
  ],
  "comment": "30 pages, 5 figures",
  "categories": [
    "math.NA",
    "gr-qc"
  ],
  "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}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-27T11:19:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N35"
    ],
    "keywords": [
      "jacobi polynomials",
      "spectral method",
      "poisson problems",
      "application",
      "discrete jacobi transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.5088J"
    }
  }
}