{
  "id": "1411.0098",
  "version": "v1",
  "published": "2014-11-01T10:41:01.000Z",
  "updated": "2014-11-01T10:41:01.000Z",
  "title": "A discontinuous-skeletal method for advection-diffusion-reaction on general meshes",
  "authors": [
    "Daniele A. Di Pietro",
    "Jérôme Droniou",
    "Alexandre Ern"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We design and analyze an approximation method for advection-diffusion-reaction equations where the (generalized) degrees of freedom are polynomials of order $k\\ge0$ at mesh faces. The method hinges on local discrete reconstruction operators for the diffusive and advective derivatives and a weak enforcement of boundary conditions. Fairly general meshes with polytopal and nonmatching cells are supported. Arbitrary polynomial orders can be considered, including the case $k=0$ which is closely related to Mimetic Finite Difference/Mixed-Hybrid Finite Volume methods. The error analysis covers the full range of P\\'eclet numbers, including the delicate case of local degeneracy where diffusion vanishes on a strict subset of the domain. Computational costs remain moderate since the use of face unknowns leads to a compact stencil with reduced communications. Numerical results are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-01T10:41:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "65N08"
    ],
    "keywords": [
      "general meshes",
      "discontinuous-skeletal method",
      "finite difference/mixed-hybrid finite volume methods",
      "mimetic finite difference/mixed-hybrid finite volume",
      "advection-diffusion-reaction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.0098D"
    }
  }
}