{
  "id": "1212.0250",
  "version": "v1",
  "published": "2012-12-02T21:44:14.000Z",
  "updated": "2012-12-02T21:44:14.000Z",
  "title": "A C^0-Weak Galerkin Finite Element Method for the Biharmonic Equation",
  "authors": [
    "Lin Mu",
    "Junping Wang",
    "Xiu Ye",
    "Shangyou Zhang"
  ],
  "comment": "21 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "A C^0-weak Galerkin (WG) method is introduced and analyzed for solving the biharmonic equation in 2D and 3D. A weak Laplacian is defined for C^0 functions in the new weak formulation. This WG finite element formulation is symmetric, positive definite and parameter free. Optimal order error estimates are established in both a discrete H^2 norm and the L^2 norm, for the weak Galerkin finite element solution. Numerical results are presented to confirm the theory. As a technical tool, a refined Scott-Zhang interpolation operator is constructed to assist the corresponding error estimate. This refined interpolation preserves the volume mass of order (k+1-d) and the surface mass of order (k+2-d) for the P_{k+2} finite element functions in d-dimensional space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-02T21:44:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "65N15",
      "35B45"
    ],
    "keywords": [
      "galerkin finite element method",
      "biharmonic equation",
      "weak galerkin finite element solution",
      "optimal order error estimates",
      "wg finite element formulation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.0250M"
    }
  }
}