{
  "id": "math/0509274",
  "version": "v2",
  "published": "2005-09-13T09:49:19.000Z",
  "updated": "2006-06-12T17:03:04.000Z",
  "title": "Error estimate for the Finite Volume Scheme applied to the advection equation",
  "authors": [
    "Benoit Merlet",
    "Julien Vovelle"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the convergence of a Finite Volume scheme for the linear advection equation with a Lipschitz divergence-free speed in $\\R^d$. We prove a $h^{1/2}$-error estimate in the $L^\\infty(0,t;L^1)$-norm for $BV$ data. This result was expected from numerical experiments and is optimal.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-06-12T17:03:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L65",
      "65M15"
    ],
    "keywords": [
      "finite volume scheme",
      "error estimate",
      "linear advection equation",
      "lipschitz divergence-free",
      "convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9274M"
    }
  }
}