{
  "id": "1406.2281",
  "version": "v2",
  "published": "2014-06-09T18:55:09.000Z",
  "updated": "2014-11-26T21:20:12.000Z",
  "title": "A PDE approach to fractional diffusion: a posteriori error analysis",
  "authors": [
    "Long Chen",
    "Ricardo H. Nochetto",
    "Enrique Otárola",
    "Abner J. Salgado"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We derive a computable a posteriori error estimator for the $\\alpha$-harmonic extension problem, which localizes the fractional powers of elliptic operators supplemented with Dirichlet boundary conditions. Our a posteriori error estimator relies on the solution of small discrete problems on anisotropic cylindrical stars. It exhibits built-in flux equilibration and is equivalent to the energy error up to data oscillation, under suitable assumptions. We design a simple adaptive algorithm and present numerical experiments which reveal a competitive performance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-09T18:55:09.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-26T21:20:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J70",
      "65N12",
      "65N30",
      "65N50"
    ],
    "keywords": [
      "posteriori error analysis",
      "fractional diffusion",
      "pde approach",
      "posteriori error estimator relies",
      "dirichlet boundary conditions"
    ],
    "publication": {
      "doi": "10.1016/j.jcp.2015.01.001",
      "journal": "Journal of Computational Physics",
      "year": 2015,
      "month": "Jul",
      "volume": 293,
      "pages": 339
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015JCoPh.293..339C"
    }
  }
}