{
  "id": "2206.09525",
  "version": "v1",
  "published": "2022-06-20T01:02:03.000Z",
  "updated": "2022-06-20T01:02:03.000Z",
  "title": "Finite Element de Rham and Stokes Complexes in Three Dimensions",
  "authors": [
    "Long Chen",
    "Xuehai Huang"
  ],
  "comment": "44 pages. arXiv admin note: text overlap with arXiv:2111.10712",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "Finite element de Rham complexes and finite element Stokes complexes with various smoothness in three dimensions are systematically constructed. First smooth scalar finite elements in three dimensions are derived through a non-overlapping decomposition of the simplicial lattice. Based on the smooth scalar finite elements, both H(div)-conforming finite elements and H(curl)-conforming finite elements with various smoothness are devised, which induce the finite element de Rham complexes with various smoothness and the associated commutative diagrams. The div stability is established for the H(div)-conforming finite elements, and the exactness of these finite element complexes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-20T01:02:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "58J10",
      "65N12"
    ],
    "keywords": [
      "dimensions",
      "first smooth scalar finite elements",
      "finite element stokes complexes",
      "rham complexes",
      "finite element complexes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}