{
  "id": "2212.12783",
  "version": "v1",
  "published": "2022-12-24T17:20:26.000Z",
  "updated": "2022-12-24T17:20:26.000Z",
  "title": "An $L^p$-primal-dual finite element method for first-order transport problems",
  "authors": [
    "Dan Li",
    "Chunmei Wang",
    "Junping Wang"
  ],
  "comment": "26 pages, 7 figures, 10 tables. arXiv admin note: text overlap with arXiv:1906.07336",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "A new $L^p$-primal-dual weak Galerkin method ($L^p$-PDWG) with $p>1$ is proposed for the first-order transport problems. The existence and uniqueness of the $L^p$-PDWG numerical solutions is established. In addition, the $L^p$-PDWG method offers a numerical solution which retains mass conservation locally on each element. An optimal order error estimate is established for the primal variable. A series of numerical results are presented to verify the efficiency and accuracy of the proposed $L^p$-PDWG scheme.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-24T17:20:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "65N15",
      "65N12"
    ],
    "keywords": [
      "primal-dual finite element method",
      "first-order transport problems",
      "optimal order error estimate",
      "primal-dual weak galerkin method",
      "pdwg method offers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}