{
  "id": "2008.03793",
  "version": "v1",
  "published": "2020-08-09T19:19:28.000Z",
  "updated": "2020-08-09T19:19:28.000Z",
  "title": "A family of finite element Stokes complexes in three dimensions",
  "authors": [
    "Kaibo Hu",
    "Qian Zhang",
    "Zhimin Zhang"
  ],
  "comment": "27 pages, 1 figure",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We construct finite element Stokes complexes on tetrahedral meshes in three-dimensional space. In the lowest order case, the finite elements in the complex have 4, 18, 16, and 1 degrees of freedom, respectively. As a consequence, we obtain gradcurl-conforming finite elements and inf-sup stable Stokes pairs on tetrahedra which fit into complexes. We show that the new elements lead to convergent algorithms for solving a gradcurl model problem as well as solving the Stokes system with precise divergence-free condition. We demonstrate the validity of the algorithms by numerical experiments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-09T19:19:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "35Q60",
      "65N15",
      "35B45"
    ],
    "keywords": [
      "construct finite element stokes complexes",
      "dimensions",
      "lowest order case",
      "inf-sup stable stokes pairs",
      "gradcurl model problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}