{
  "id": "2205.13656",
  "version": "v1",
  "published": "2022-05-26T22:29:38.000Z",
  "updated": "2022-05-26T22:29:38.000Z",
  "title": "Finite difference schemes for the parabolic $p$-Laplace equation",
  "authors": [
    "Félix del Teso",
    "Erik Lindgren"
  ],
  "comment": "17 pages, 1 figure",
  "categories": [
    "math.NA",
    "cs.NA",
    "math.AP"
  ],
  "abstract": "We propose a new finite difference scheme for the degenerate parabolic equation \\[ \\partial_t u - \\mbox{div}(|\\nabla u|^{p-2}\\nabla u) =f, \\quad p\\geq 2. \\] Under the assumption that the data is H\\\"older continuous, we establish the convergence of the explicit-in-time scheme for the Cauchy problem provided a suitable stability type CFL-condition. An important advantage of our approach, is that the CFL-condition makes use of the regularity provided by the scheme to reduce the computational cost. In particular, for Lipschitz data, the CFL-condition is of the same order as for the heat equation and independent of $p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-26T22:29:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite difference scheme",
      "laplace equation",
      "degenerate parabolic equation",
      "suitable stability type cfl-condition",
      "lipschitz data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}