{
  "id": "2002.12127",
  "version": "v1",
  "published": "2020-02-27T14:40:24.000Z",
  "updated": "2020-02-27T14:40:24.000Z",
  "title": "A nonconforming pressure-robust finite element method for the Stokes equations on anisotropic meshes",
  "authors": [
    "Thomas Apel",
    "Volker Kempf",
    "Alexander Linke",
    "Christian Merdon"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "Most classical finite element schemes for the (Navier-)Stokes equations are neither pressure-robust, nor are they inf-sup stable on general anisotropic triangulations. A lack of pressure-robustness may lead to large velocity errors, whenever the Stokes momentum balance is dominated by a strong and complicated pressure gradient. It is a consequence of a method, which does not exactly satisfy the divergence constraint. However, inf-sup stable schemes can often be made pressure-robust just by a recent, modified discretization of the exterior forcing term, using $\\mathbf{H}(\\operatorname{div})$-conforming velocity reconstruction operators. This approach has so far only been analyzed on shape-regular triangulations. The novelty of the present contribution is that the reconstruction approach for the Crouzeix-Raviart method, which has a stable Fortin operator on arbitrary meshes, is combined with results on the interpolation error on anisotropic elements for reconstruction operators of Raviart-Thomas and Brezzi-Douglas-Marini type, generalizing the method to a large class of anisotropic triangulations. Numerical examples confirm the theoretical results in a 2D and a 3D test case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-27T14:40:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "65N15",
      "65D05"
    ],
    "keywords": [
      "nonconforming pressure-robust finite element method",
      "stokes equations",
      "anisotropic meshes",
      "3d test case",
      "general anisotropic triangulations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}