{
  "id": "2210.02756",
  "version": "v1",
  "published": "2022-10-06T08:48:23.000Z",
  "updated": "2022-10-06T08:48:23.000Z",
  "title": "Pressure-robust and conforming discretization of the Stokes equations on anisotropic meshes",
  "authors": [
    "Volker Kempf"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "Pressure-robust discretizations for incompressible flows have been in the focus of research for the past years. Many publications construct exactly divergence-free methods or use a reconstruction approach [13] for existing methods like the Crouzeix--Raviart element in order to achieve pressure-robustness. To the best of our knowledge, except for our recent publications [3,4], all those articles impose a condition on the shape-regularity of the mesh, and the two mentioned papers that allow for anisotropic elements use a non-conforming velocity approximation. Based on the classical Bernardi--Raugel element we provide a conforming pressure-robust discretization using the reconstruction approach on anisotropic meshes. Numerical examples support the theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-06T08:48:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "anisotropic meshes",
      "stokes equations",
      "conforming discretization",
      "pressure-robust discretization",
      "publications construct exactly divergence-free methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}