{
  "id": "2208.01770",
  "version": "v1",
  "published": "2022-08-02T21:57:53.000Z",
  "updated": "2022-08-02T21:57:53.000Z",
  "title": "An $L^p$- Primal-Dual Weak Galerkin method for div-curl Systems",
  "authors": [
    "Waixiang Cao",
    "Chunmei Wang",
    "Junping Wang"
  ],
  "comment": "22 pages, 2 figures, 8 tables. arXiv admin note: text overlap with arXiv:2101.03466",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "This paper presents a new $L^p$-primal-dual weak Galerkin (PDWG) finite element method for the div-curl system with the normal boundary condition for $p>1$. Two crucial features for the proposed $L^p$-PDWG finite element scheme are as follows: (1) it offers an accurate and reliable numerical solution to the div-curl system under the low $W^{\\alpha, p}$-regularity ($\\alpha>0$) assumption for the exact solution; (2) it offers an effective approximation of the normal harmonic vector fields on domains with complex topology. An optimal order error estimate is established in the $L^q$-norm for the primal variable where $\\frac{1}{p}+\\frac{1}{q}=1$. A series of numerical experiments are presented to demonstrate the performance of the proposed $L^p$-PDWG algorithm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-02T21:57:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "35Q60"
    ],
    "keywords": [
      "primal-dual weak galerkin method",
      "div-curl system",
      "pdwg finite element scheme",
      "optimal order error estimate",
      "normal harmonic vector fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}