{
  "id": "1610.05850",
  "version": "v1",
  "published": "2016-10-19T02:36:32.000Z",
  "updated": "2016-10-19T02:36:32.000Z",
  "title": "Discretization of mixed formulations of elliptic problems on polyhedral meshes",
  "authors": [
    "Konstantin Lipnikov",
    "Gianmarco Manzini"
  ],
  "comment": "27 pages; 4 figures; 49 citations",
  "journal": "Lecture Notes in Computational Science and Engineering, vol. 114, pag. 309-340, 2016",
  "categories": [
    "math.NA"
  ],
  "abstract": "We review basic design principles underpinning the construction of mimetic finite difference and a few finite volume and finite element schemes for mixed formulations of elliptic problems. For a class of low-order mixed-hybrid schemes, we show connections between these principles and prove that the consistency and stability conditions must lead to a member of the mimetic family of schemes regardless of the selected discretization framework. Finally, we give two examples of using flexibility of the mimetic framework: derivation of higher-order schemes and convergent schemes for nonlinear problems with small diffusion coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-19T02:36:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M06",
      "65M08",
      "65M99"
    ],
    "keywords": [
      "elliptic problems",
      "mixed formulations",
      "polyhedral meshes",
      "discretization",
      "review basic design principles underpinning"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}