{
  "id": "2103.14924",
  "version": "v1",
  "published": "2021-03-27T14:57:29.000Z",
  "updated": "2021-03-27T14:57:29.000Z",
  "title": "A Construction of $C^r$ Conforming Finite Element Spaces in Any Dimension",
  "authors": [
    "Jun Hu",
    "Ting Lin",
    "Qingyu Wu"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "This paper proposes a construction of local $C^r$ interpolation spaces and $C^r$ conforming finite element spaces with arbitrary $r$ in any dimension. It is shown that if $k \\ge 2^{d}r+1$ the space $\\mathcal P_k$ of polynomials of degree $\\le k$ can be taken as the shape function space of $C^r$ finite element spaces in $d$ dimensions. This is the first work on constructing such $C^r$ conforming finite elements in any dimension in a unified way. It solves a long-standing open problem in finite element methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-27T14:57:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conforming finite element spaces",
      "construction",
      "shape function space",
      "finite element methods",
      "first work"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}