{
  "id": "1401.1020",
  "version": "v1",
  "published": "2014-01-06T09:40:17.000Z",
  "updated": "2014-01-06T09:40:17.000Z",
  "title": "Gradient entropy estimate and convergence of a semi-explicit scheme for diagonal hyperbolic systems",
  "authors": [
    "Laurent Monasse",
    "Régis Monneau"
  ],
  "comment": "22 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "In this paper, we consider diagonal hyperbolic systems with monotone continuous initial data. We propose a natural semi-explicit and upwind first order scheme. Under a certain non-negativity condition on the Jacobian matrix of the velocities of the system, there is a gradient entropy estimate for the hyperbolic system. We show that our scheme enjoys a similar gradient entropy estimate at the discrete level. This property allows us to prove the convergence of the scheme.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-06T09:40:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M12",
      "35L60",
      "35L45",
      "35A02"
    ],
    "keywords": [
      "diagonal hyperbolic systems",
      "semi-explicit scheme",
      "convergence",
      "similar gradient entropy estimate",
      "upwind first order scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.1020M"
    }
  }
}