{
  "id": "2305.11356",
  "version": "v1",
  "published": "2023-05-19T00:14:31.000Z",
  "updated": "2023-05-19T00:14:31.000Z",
  "title": "A Mixed Finite Element Method for the Biharmonic Equation with Hybridization",
  "authors": [
    "Long Chen",
    "Xuehai Huang"
  ],
  "comment": "28 pages",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "A new $H(\\textrm{divdiv})$-conforming finite element is presented, which avoids the need for super-smoothness by redistributing the degrees of freedom to edges and faces. This leads to a hybridizable mixed method for the biharmonic equation. Moreover, new weak Galerkin and $C^0$ discontinuous Galerkin methods for the biharmonic equation are derived. Finally, new finite element divdiv complexes are established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-19T00:14:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "58J10",
      "65N12",
      "65N15"
    ],
    "keywords": [
      "mixed finite element method",
      "biharmonic equation",
      "finite element divdiv complexes",
      "hybridization",
      "weak galerkin"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}