{
  "id": "1405.4715",
  "version": "v2",
  "published": "2014-05-19T13:23:44.000Z",
  "updated": "2018-08-27T02:46:00.000Z",
  "title": "Convergence of a hybrid scheme for the elliptic Monge-Ampere equation",
  "authors": [
    "Gerard Awanou"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We prove the convergence of a hybrid discretization to the viscosity solution of the elliptic Monge-Ampere equation. The hybrid discretization uses a standard finite difference discretization in parts of the computational domain where the solution is expected to be smooth and a monotone scheme elsewhere. A motivation for the hybrid discretization is the lack of an appropriate Newton solver for the standard finite difference discretization on the whole domain.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-19T13:23:44.000Z",
      "abstract": "We prove the convergence of a hybrid discretization to the viscosity solution of the elliptic Monge-Amp\\`ere equation. The hybrid discretization uses a standard finite difference discretization in parts of the computational domain where the solution is expected to be smooth and a monotone scheme elsewhere. A motivation for the hybrid discretization is the lack of an appropriate Newton solver for the standard finite difference discretization on the whole domain.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2018-08-27T02:46:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic monge-ampere equation",
      "hybrid scheme",
      "standard finite difference discretization",
      "hybrid discretization",
      "convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.4715A"
    }
  }
}