{
  "id": "2410.20615",
  "version": "v1",
  "published": "2024-10-27T22:23:45.000Z",
  "updated": "2024-10-27T22:23:45.000Z",
  "title": "Efficient Weak Galerkin Finite Element Methods for Maxwell Equations on polyhedral Meshes without Convexity Constraints",
  "authors": [
    "Chunmei Wang",
    "Shangyou Zhang"
  ],
  "comment": "31 pages, 6 tables",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "This paper presents an efficient weak Galerkin (WG) finite element method with reduced stabilizers for solving the time-harmonic Maxwell equations on both convex and non-convex polyhedral meshes. By employing bubble functions as a critical analytical tool, the proposed method enhances efficiency by partially eliminating the stabilizers traditionally used in WG methods. This streamlined WG method demonstrates stability and effectiveness on convex and non-convex polyhedral meshes, representing a significant improvement over existing stabilizer-free WG methods, which are typically limited to convex elements within finite element partitions. The method achieves an optimal error estimate for the exact solution in a discrete $H^1$ norm, and additionally, an optimal $L^2$ error estimate is established for the WG solution. Several numerical experiments are conducted to validate the method's efficiency and accuracy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-27T22:23:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "65N15",
      "65N12",
      "74N20",
      "35B45",
      "35J50",
      "65N30",
      "65N15",
      "65N12",
      "74N20",
      "35B45",
      "35J50",
      "35J35"
    ],
    "keywords": [
      "weak galerkin finite element methods",
      "efficient weak galerkin finite element",
      "polyhedral meshes",
      "maxwell equations",
      "convexity constraints"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}