{
  "id": "1002.0887",
  "version": "v1",
  "published": "2010-02-04T02:58:41.000Z",
  "updated": "2010-02-04T02:58:41.000Z",
  "title": "Convergence and Optimal Complexity of Adaptive Finite Element Methods",
  "authors": [
    "Lianhua He",
    "Aihui Zhou"
  ],
  "comment": "30pages, 14figures",
  "categories": [
    "math.NA"
  ],
  "abstract": "In this paper, we study adaptive finite element approximations in a perturbation framework, which makes use of the existing adaptive finite element analysis of a linear symmetric elliptic problem. We prove the convergence and complexity of adaptive finite element methods for a class of elliptic partial differential equations. For illustration, we apply the general approach to obtain the convergence and complexity of adaptive finite element methods for a nonsymmetric problem, a nonlinear problem as well as an unbounded coefficient eigenvalue problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-02-04T02:58:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N15",
      "65N25",
      "65N30"
    ],
    "keywords": [
      "adaptive finite element methods",
      "optimal complexity",
      "adaptive finite element analysis",
      "convergence",
      "study adaptive finite element approximations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.0887H"
    }
  }
}