{
  "id": "2011.12377",
  "version": "v1",
  "published": "2020-11-24T20:50:50.000Z",
  "updated": "2020-11-24T20:50:50.000Z",
  "title": "Low Regularity Primal-Dual Weak Galerkin Finite Element Methods for Ill-Posed Elliptic Cauchy Problems",
  "authors": [
    "Chunmei Wang"
  ],
  "comment": "20 pages, 18 tables",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "A new primal-dual weak Galerkin (PDWG) finite element method is introduced and analyzed for the ill-posed elliptic Cauchy problems with ultra-low regularity assumptions on the exact solution. The Euler-Lagrange formulation resulting from the PDWG scheme yields a system of equations involving both the primal equation and the adjoint (dual) equation. The optimal order error estimate for the primal variable in a low regularity assumption is established. A series of numerical experiments are illustrated to validate effectiveness of the developed theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-24T20:50:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "65N15",
      "65N12",
      "74N20"
    ],
    "keywords": [
      "weak galerkin finite element methods",
      "regularity primal-dual weak galerkin finite",
      "low regularity primal-dual weak galerkin",
      "primal-dual weak galerkin finite element",
      "ill-posed elliptic cauchy problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}