{
  "id": "1310.8084",
  "version": "v1",
  "published": "2013-10-30T09:53:42.000Z",
  "updated": "2013-10-30T09:53:42.000Z",
  "title": "Stability Analysis for Discontinuous Galerkin approximations of the elastodynamics problem",
  "authors": [
    "Paola F. Antonietti",
    "Blanca Ayuso de Dios",
    "Ilario Mazzieri",
    "Alfio Quarteroni"
  ],
  "comment": "32 pages, 4 figures",
  "categories": [
    "math.NA"
  ],
  "abstract": "We consider semi-discrete discontinuous Galerkin approximations of a general elastodynamics problem, in both {\\it displacement} and {\\it displacement-stress} formulations. We present the stability analysis of all the methods in the natural energy norm and derive optimal a-priori error estimates. For the displacement-stress formulation, schemes preserving the total energy of the system are introduced and discussed. We include some numerical experiments in three dimensions to verify the theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-30T09:53:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M60",
      "73V05",
      "65M10"
    ],
    "keywords": [
      "stability analysis",
      "derive optimal a-priori error estimates",
      "natural energy norm",
      "general elastodynamics problem",
      "semi-discrete discontinuous galerkin approximations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.8084A"
    }
  }
}