{
  "id": "1006.3319",
  "version": "v1",
  "published": "2010-06-16T20:14:20.000Z",
  "updated": "2010-06-16T20:14:20.000Z",
  "title": "Convergence of an adaptive Kačanov FEM for quasi-linear problems",
  "authors": [
    "Eduardo M. Garau",
    "Pedro Morin",
    "Carlos Zuppa"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We design an adaptive finite element method to approximate the solutions of quasi-linear elliptic problems. The algorithm is based on a Ka\\v{c}anov iteration and a mesh adaptation step is performed after each linear solve. The method is thus \\emph{inexact} because we do not solve the discrete nonlinear problems exactly, but rather perform one iteration of a fixed point method (Ka\\v{c}anov), using the approximation of the previous mesh as an initial guess. The convergence of the method is proved for any \\emph{reasonable} marking strategy and starting from any initial mesh. We conclude with some numerical experiments that illustrate the theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-16T20:14:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "adaptive kačanov fem",
      "quasi-linear problems",
      "convergence",
      "adaptive finite element method",
      "quasi-linear elliptic problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.3319G"
    }
  }
}