{
  "id": "1010.1251",
  "version": "v1",
  "published": "2010-10-06T19:58:27.000Z",
  "updated": "2010-10-06T19:58:27.000Z",
  "title": "Quasi-optimal convergence rate of an AFEM for quasi-linear problems",
  "authors": [
    "Eduardo M. Garau",
    "Pedro Morin",
    "Carlos Zuppa"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We prove the quasi-optimal convergence of a standard adaptive finite element method (AFEM) for nonlinear elliptic second-order equations of monotone type. The adaptive algorithm is based on residual-type a posteriori error estimators and D\\\"orfler's strategy is assumed for marking. We first prove a contraction property for a suitable definition of total error, which is equivalent to the total error as defined by Casc\\'on et al. (in SIAM J. Numer. Anal. 46 (2008), 2524--2550), and implies linear convergence of the algorithm. Secondly, we use this contraction to derive the optimal cardinality of the AFEM.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-06T19:58:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quasi-optimal convergence rate",
      "quasi-linear problems",
      "nonlinear elliptic second-order equations",
      "standard adaptive finite element method",
      "total error"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.1251G"
    }
  }
}