{
  "id": "1803.01979",
  "version": "v1",
  "published": "2018-03-06T01:30:47.000Z",
  "updated": "2018-03-06T01:30:47.000Z",
  "title": "A Virtual Element Method for the Transmission Eigenvalue Problem",
  "authors": [
    "David Mora",
    "Iván Velásquez"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "In this paper, we analyze a virtual element method (VEM) for solving a non-selfadjoint fourth-order eigenvalue problem derived from the transmission eigenvalue problem. We write a variational formulation and propose a $C^1$-conforming discretization by means of the VEM. We use the classical approximation theory for compact non-selfadjoint operators to obtain optimal order error estimates for the eigenfunctions and a double order for the eigenvalues. Finally, we present some numerical experiments illustrating the behavior of the virtual scheme on different families of meshes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-06T01:30:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N25",
      "65N30",
      "65N21",
      "78A46"
    ],
    "keywords": [
      "transmission eigenvalue problem",
      "virtual element method",
      "optimal order error estimates",
      "non-selfadjoint fourth-order eigenvalue problem",
      "compact non-selfadjoint operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}