{
  "id": "1809.10354",
  "version": "v1",
  "published": "2018-09-27T05:54:24.000Z",
  "updated": "2018-09-27T05:54:24.000Z",
  "title": "Geometric Transformation of Finite Element Methods: Theory and Applications",
  "authors": [
    "M. Holst",
    "M. Licht"
  ],
  "comment": "21 pages, 2 figures, 2 tables",
  "categories": [
    "math.NA"
  ],
  "abstract": "We present a new technique to apply finite element methods to partial differential equations over curved domains. A change of variables along a coordinate transformation satisfying only low regularity assumptions can translate a Poisson problem over a curved physical domain to a Poisson problem over a polyhedral parametric domain. This greatly simplifies both the geometric setting and the practical implementation, at the cost of having globally rough non-trivial coefficients and data in the parametric Poisson problem. Our main result is that a recently developed broken Bramble-Hilbert lemma is key in harnessing regularity in the physical problem to prove higher-order finite element convergence rates for the parametric problem. Numerical experiments are given which confirm the predictions of our theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-27T05:54:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite element methods",
      "geometric transformation",
      "higher-order finite element convergence rates",
      "applications",
      "globally rough non-trivial coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}