{
  "id": "1502.07658",
  "version": "v1",
  "published": "2015-02-26T18:09:45.000Z",
  "updated": "2015-02-26T18:09:45.000Z",
  "title": "A posteriori error estimation in a finite element method for reconstruction of dielectric permittivity",
  "authors": [
    "John Bondestam Malmberg"
  ],
  "comment": "17 pages, 1 figure",
  "categories": [
    "math.NA"
  ],
  "abstract": "We present a posteriori error estimates for finite element approximations in a minimization approach to a coefficient inverse problem. The problem is that of reconstructing the dielectric permittivity $\\varepsilon = \\varepsilon(\\mathbf{x})$, $\\mathbf{x}\\in\\Omega\\subset\\mathbb{R}^3$, from boundary measurements of the electric field. The electric field is related to the permittivity via Maxwell's equations. The reconstruction procedure is based on minimization of a Tikhonov functional where the permittivity, the electric field and a Lagrangian multiplier function are approximated by peicewise polynomials. Our main result is an estimate for the difference between the computed coefficient $\\varepsilon_h$ and the true minimizer $\\varepsilon$, in terms of the computed functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-26T18:09:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N15",
      "65N21",
      "65N30"
    ],
    "keywords": [
      "finite element method",
      "posteriori error estimation",
      "dielectric permittivity",
      "electric field",
      "reconstruction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}