{
  "id": "1204.2145",
  "version": "v3",
  "published": "2012-04-10T13:39:15.000Z",
  "updated": "2013-10-28T22:43:07.000Z",
  "title": "Finite element approximation of steady flows of incompressible fluids with implicit power-law-like rheology",
  "authors": [
    "Lars Diening",
    "Christian Kreuzer",
    "Endre Süli"
  ],
  "comment": "32 pages",
  "journal": "SIAM J. Numer. Anal. 51(2) (2013) 984-1015",
  "categories": [
    "math.NA"
  ],
  "abstract": "We develop the analysis of finite element approximations of implicit power-law-like models for viscous incompressible fluids. The Cauchy stress and the symmetric part of the velocity gradient in the class of models under consideration are related by a, possibly multi--valued, maximal monotone $r$-graph, with $1<r<\\infty$. Using a variety of weak compactness techniques, including Chacon's biting lemma and Young measures, we show that a subsequence of the sequence of finite element solutions converges to a weak solution of the problem as the finite element discretization parameter $h$ tends to 0. A key new technical tool in our analysis is a finite element counterpart of the Acerbi--Fusco Lipschitz truncation of Sobolev functions.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-10-28T22:43:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "65N12",
      "76A05",
      "35Q35"
    ],
    "keywords": [
      "finite element approximation",
      "implicit power-law-like rheology",
      "incompressible fluids",
      "steady flows",
      "finite element solutions converges"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.2145D"
    }
  }
}