{
  "id": "1311.5121",
  "version": "v2",
  "published": "2013-11-20T16:23:18.000Z",
  "updated": "2014-08-12T12:38:19.000Z",
  "title": "Finite element approximation of the $p(\\cdot)$-Laplacian",
  "authors": [
    "D. Breit",
    "L. Diening",
    "S. Schwarzacher"
  ],
  "categories": [
    "math.NA",
    "math.AP"
  ],
  "abstract": "We study a~priori estimates for the Dirichlet problem of the $p(\\cdot)$-Laplacian, \\[-\\mathrm{div}(|\\nabla v|^{p(\\cdot)-2} \\nabla v) = f. \\] We show that the gradients of the finite element approximation with zero boundary data converges with rate $O(h^\\alpha)$ if the exponent $p$ is $\\alpha$-H\\\"{o}lder continuous. The error of the gradients is measured in the so-called quasi-norm, i.e. we measure the $L^2$-error of $|\\nabla v|^{\\frac{p-2}{2}} \\nabla v$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-12T12:38:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N15",
      "65N30",
      "65D05",
      "35J60",
      "46E30"
    ],
    "keywords": [
      "finite element approximation",
      "zero boundary data converges",
      "dirichlet problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.5121B"
    }
  }
}