{
  "id": "1402.4454",
  "version": "v2",
  "published": "2014-02-18T19:57:52.000Z",
  "updated": "2014-09-16T19:28:15.000Z",
  "title": "An Interior Penalty Method with $C^0$ Finite Elements for the Approximation of the Maxwell Equations in Heterogeneous Media: Convergence Analysis with Minimal Regularity",
  "authors": [
    "Andrea Bonito",
    "Jean-Luc Guermond",
    "Francky Luddens"
  ],
  "comment": "34 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "The present paper proposes and analyzes an interior penalty technique using $C^0$-finite elements to solve the Maxwell equations in domains with heterogeneous properties. The convergence analysis for the boundary value problem and the eigenvalue problem is done assuming only minimal regularity in Lipschitz domains. The method is shown to converge for any polynomial degrees and to be spectrally correct.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-18T19:57:52.000Z",
      "title": "$\\mathbf{H}^1$-conforming approximation of the Maxwell equations in heterogeneous media with minimal regularity",
      "abstract": "The present paper proposes and analyzes a nodal $C^0$-finite element technique to solve the Maxwell equations in domains with heterogeneous properties. The convergence analysis is done assuming only minimal regularity in Lipschitz domains. The method is shown to converge for any polynomial degrees and is spectrally correct.",
      "comment": "31 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-16T19:28:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N25",
      "65F15",
      "35Q60"
    ],
    "keywords": [
      "minimal regularity",
      "maxwell equations",
      "conforming approximation",
      "heterogeneous media",
      "finite element technique"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.4454B"
    }
  }
}