{
  "id": "2010.09666",
  "version": "v1",
  "published": "2020-10-19T17:02:01.000Z",
  "updated": "2020-10-19T17:02:01.000Z",
  "title": "Error analysis for a finite difference scheme for axisymmetric mean curvature flow of genus-0 surfaces",
  "authors": [
    "Klaus Deckelnick",
    "Robert Nürnberg"
  ],
  "comment": "24 pages, 3 figures",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We consider a finite difference approximation of mean curvature flow for axisymmetric surfaces of genus zero. A careful treatment of the degeneracy at the axis of rotation for the one dimensional partial differential equation for a parameterization of the generating curve allows us to prove error bounds with respect to discrete $L^2$-- and $H^1$--norms for a fully discrete approximation. The theoretical results are confirmed with the help of numerical convergence experiments. We also present numerical simulations for some genus-0 surfaces, including for a non-embedded self-shrinker for mean curvature flow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-19T17:02:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M60",
      "65M12",
      "65M15",
      "53C44",
      "35K55"
    ],
    "keywords": [
      "axisymmetric mean curvature flow",
      "finite difference scheme",
      "error analysis",
      "dimensional partial differential equation",
      "finite difference approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}