{
  "id": "1201.1632",
  "version": "v1",
  "published": "2012-01-08T13:29:17.000Z",
  "updated": "2012-01-08T13:29:17.000Z",
  "title": "Metric tensors for the interpolation error and its gradient in $L^p$ norm",
  "authors": [
    "Xiaobo Yin",
    "Hehu Xie"
  ],
  "comment": "19 pages, 24 figures",
  "categories": [
    "math.NA"
  ],
  "abstract": "A uniform strategy to derive metric tensors in two spatial dimension for interpolation errors and their gradients in $L^p$ norm is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in corresponding metric space, with the metric tensor being computed based on a posteriori error estimates in different norms. Numerical results show that the corresponding convergence rates are always optimal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-01-08T13:29:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "65N50"
    ],
    "keywords": [
      "interpolation error",
      "generates anisotropic adaptive meshes",
      "posteriori error estimates",
      "uniform strategy",
      "derive metric tensors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}