{
  "id": "2211.08656",
  "version": "v1",
  "published": "2022-11-16T04:15:22.000Z",
  "updated": "2022-11-16T04:15:22.000Z",
  "title": "Complexes from Complexes: Finite Element Complexes in Three Dimensions",
  "authors": [
    "Long Chen",
    "Xuehai Huang"
  ],
  "comment": "44 pages",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "Finite element Hessian, elasticity, and divdiv complexes are systematically derived via Bernstein-Gelfand-Gelfand (BGG) framework developed by Arnold and Hu [Complexes from complexes. {\\em Found. Comput. Math.}, 2021]. Our construction is built on three major tools: smooth finite element de Rham complexes, the $t-n$ decomposition approach for constructing div-conforming elements, and the trace complexes and corresponding 2D finite element complexes. Two reduction operators are introduced to solve the mis-match of continuity of the BGG diagram in the continuous level.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-16T04:15:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "58J10",
      "65N12"
    ],
    "keywords": [
      "corresponding 2d finite element complexes",
      "dimensions",
      "finite element hessian",
      "smooth finite element",
      "rham complexes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}