{
  "id": "1805.05142",
  "version": "v1",
  "published": "2018-05-14T12:36:49.000Z",
  "updated": "2018-05-14T12:36:49.000Z",
  "title": "Stable non-symmetric coupling of the finite volume and the boundary element method for convection-dominated parabolic-elliptic interface problems",
  "authors": [
    "Christoph Erath",
    "Robert Schorr"
  ],
  "comment": "26 pages, 3 figures",
  "categories": [
    "math.NA"
  ],
  "abstract": "Many problems in electrical engineering or fluid mechanics can be modeled by parabolic-elliptic interface problems, where the domain for the exterior elliptic problem might be unbounded. A possibility to solve this class of problems numerically is the non-symmetric coupling of finite elements (FEM) and boundary elements (BEM) analyzed in [Egger, Erath, Schorr, arXiv:1711.08487, 2017]. If, for example, the interior problem represents a fluid, this method is not appropriate since FEM in general lacks conservation of numerical fluxes and in case of convection dominance also stability. A possible remedy to guarantee both is the use of the vertex-centered finite volume method (FVM) with an upwind stabilization option. Thus we propose a (non-symmetric) coupling of FVM and BEM for a semi-discretization of the underlying problem. For the subsequent time discretization we introduce two options: a variant of the backward Euler method which allows us to develop an analysis under minimal regularity assumptions and the classical backward Euler method. We analyze both, the semi-discrete and the fully discrete system, in terms of convergence and error estimates. Some numerical examples illustrate the theoretical findings and give some ideas for practical applications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-14T12:36:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N08",
      "65N38",
      "65N40",
      "65N12",
      "65N15",
      "82B24"
    ],
    "keywords": [
      "convection-dominated parabolic-elliptic interface problems",
      "boundary element method",
      "finite volume",
      "stable non-symmetric coupling",
      "backward euler method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}