{
  "id": "0810.3590",
  "version": "v1",
  "published": "2008-10-20T15:44:54.000Z",
  "updated": "2008-10-20T15:44:54.000Z",
  "title": "On the convergence of the hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces",
  "authors": [
    "Alexei Bespalov",
    "Norbert Heuer"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "In this paper the hp-version of the boundary element method is applied to the electric field integral equation on a piecewise plane (open or closed) Lipschitz surface. The underlying meshes are supposed to be quasi-uniform. We use H(div)-conforming discretisations with quadrilateral elements of Raviart-Thomas type and establish quasi-optimal convergence of hp-approximations. Main ingredient of our analysis is a new H^{-1/2}(div)-conforming p-interpolation operator that assumes only H^r \\cap H^{-1/2}(div)-regularity (r > 0) and for which we show quasi-stability with respect to polynomial degrees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-20T15:44:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N38",
      "65N12",
      "78M15",
      "41A10"
    ],
    "keywords": [
      "electric field integral equation",
      "polyhedral surfaces",
      "quasi-uniform meshes",
      "convergence",
      "boundary element method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.3590B"
    }
  }
}