{
  "id": "1504.02647",
  "version": "v1",
  "published": "2015-04-10T12:02:23.000Z",
  "updated": "2015-04-10T12:02:23.000Z",
  "title": "The BEM with graded meshes for the electric field integral equation on polyhedral surfaces",
  "authors": [
    "Alex Bespalov",
    "Serge Nicaise"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We consider the variational formulation of the electric field integral equation on a Lipschitz polyhedral surface $\\Gamma$. We study the Galerkin boundary element discretisations based on the lowest-order Raviart-Thomas surface elements on a sequence of anisotropic meshes algebraically graded towards the edges of $\\Gamma$. We establish quasi-optimal convergence of Galerkin solutions under a mild restriction on the strength of grading. The key ingredient of our convergence analysis are new componentwise stability properties of the Raviart-Thomas interpolant on anisotropic elements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-10T12:02:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N38",
      "65N12",
      "78M15"
    ],
    "keywords": [
      "electric field integral equation",
      "graded meshes",
      "lowest-order raviart-thomas surface elements",
      "galerkin boundary element discretisations",
      "lipschitz polyhedral surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150402647B"
    }
  }
}