{
  "id": "1310.6573",
  "version": "v4",
  "published": "2013-10-24T11:51:59.000Z",
  "updated": "2013-11-28T09:41:15.000Z",
  "title": "Multigrid algorithms for $hp$-Discontinuous Galerkin discretizations of elliptic problems",
  "authors": [
    "P. F. Antonietti",
    "M. Sarti",
    "M. Verani"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We present W-cycle multigrid algorithms for the solution of the linear system of equations arising from a wide class of $hp$-version discontinuous Galerkin discretizations of elliptic problems. Starting from a classical framework in multigrid analysis, we define a smoothing and an approximation property, which are used to prove the uniform convergence of the W-cycle scheme with respect to the granularity of the grid and the number of levels. The dependence of the convergence rate on the polynomial approximation degree $p$ is also tracked, showing that the contraction factor of the scheme deteriorates with increasing $p$. A discussion on the effects of employing inherited or non-inherited sublevel solvers is also presented. Numerical experiments confirm the theoretical results.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-11-28T09:41:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic problems",
      "w-cycle multigrid algorithms",
      "version discontinuous galerkin discretizations",
      "polynomial approximation degree",
      "numerical experiments confirm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.6573A"
    }
  }
}