{
  "id": "2101.01398",
  "version": "v1",
  "published": "2021-01-05T08:05:36.000Z",
  "updated": "2021-01-05T08:05:36.000Z",
  "title": "On the convergence rate of the Kačanov scheme for shear-thinning fluids",
  "authors": [
    "Pascal Heid",
    "Endre Süli"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We explore the convergence rate of the Ka\\v{c}anov iteration scheme for different models of shear-thinning fluids, including Carreau and power-law type explicit quasi-Newtonian constitutive laws. It is shown that the energy difference contracts along the sequence generated by the iteration. In addition, an a posteriori computable contraction factor is proposed, which improves previously derived bounds on the contraction factor in the context of the power-law model. Significantly, this factor is shown to be independent of the choice of the cut-off parameters whose use was proposed in the literature for the Ka\\v{c}anov iteration applied to the power-law model. Our analytical findings are confirmed by a series of numerical experiments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-05T08:05:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65J15",
      "35Q35",
      "35J62"
    ],
    "keywords": [
      "convergence rate",
      "shear-thinning fluids",
      "kačanov scheme",
      "power-law type explicit quasi-newtonian",
      "power-law model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}