{
  "id": "0708.2116",
  "version": "v1",
  "published": "2007-08-15T23:21:09.000Z",
  "updated": "2007-08-15T23:21:09.000Z",
  "title": "A posteriori error estimates for finite element approximations of the Cahn-Hilliard equation and the Hele-Shaw flow",
  "authors": [
    "Xiaobing Feng",
    "Haijun Wu"
  ],
  "comment": "29 pages and 7 figures",
  "categories": [
    "math.NA",
    "math.AP"
  ],
  "abstract": "This paper develops a posteriori error estimates of residual type for conforming and mixed finite element approximations of the fourth order Cahn-Hilliard equation $u_t+\\De\\bigl(\\eps \\De u-\\eps^{-1} f(u)\\bigr)=0$. It is shown that the {\\it a posteriori} error bounds depends on $\\eps^{-1}$ only in some low polynomial order, instead of exponential order. Using these a posteriori error estimates, we construct an adaptive algorithm for computing the solution of the Cahn-Hilliard equation and its sharp interface limit, the Hele-Shaw flow. Numerical experiments are presented to show the robustness and effectiveness of the new error estimators and the proposed adaptive algorithm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-08-15T23:21:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M60",
      "65M12",
      "65M15",
      "53A10"
    ],
    "keywords": [
      "posteriori error estimates",
      "hele-shaw flow",
      "fourth order cahn-hilliard equation",
      "mixed finite element approximations",
      "sharp interface limit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.2116F"
    }
  }
}