{
  "id": "1803.09547",
  "version": "v2",
  "published": "2018-03-26T12:35:51.000Z",
  "updated": "2018-10-03T14:06:08.000Z",
  "title": "A new probabilistic interpretation of Bramble-Hilbert lemma",
  "authors": [
    "Joël Chaskalovic",
    "Franck Assous"
  ],
  "comment": "11 Pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1803.09552",
  "categories": [
    "math.NA"
  ],
  "abstract": "The aim of this paper is to provide new perspectives on relative finite element accuracy which is usually based on the asymptotic speed of convergence comparison when the mesh size $h$ goes to zero. Starting from a geometrical reading of the error estimate due to Bramble-Hilbert lemma, we derive two probability distributions that estimate the relative accuracy, considered as a random variable, between two Lagrange finite elements $P_k$ and $P_m$, ($k < m$). We establish mathematical properties of these probabilistic distributions and we get new insights which, among others, show that $P_k$ or $P_m$ is more likely accurate than the other, depending on the value of the mesh size $h$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2018-10-03T14:06:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N15",
      "65N30",
      "65N75"
    ],
    "keywords": [
      "bramble-hilbert lemma",
      "probabilistic interpretation",
      "relative finite element accuracy",
      "lagrange finite elements",
      "convergence comparison"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}