{
  "id": "2501.02590",
  "version": "v1",
  "published": "2025-01-05T15:51:42.000Z",
  "updated": "2025-01-05T15:51:42.000Z",
  "title": "Auto-Stabilized Weak Galerkin Finite Element Methods for Stokes Equations on Non-Convex Polytopal Meshes",
  "authors": [
    "Chunmei Wang",
    "Shangyou Zhang"
  ],
  "comment": "30 pages, 8 tables, 8 figures",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "This paper introduces an auto-stabilized weak Galerkin (WG) finite element method for solving Stokes equations without relying on traditional stabilizers. The proposed WG method accommodates both convex and non-convex polytopal elements in finite element partitions, leveraging bubble functions as a key analytical tool. The simplified WG method is symmetric and positive definite, and optimal-order error estimates are derived for WG approximations in both the discrete $H^1$ norm and the $L^2$ norm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-05T15:51:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "65N15",
      "65N12",
      "65N20"
    ],
    "keywords": [
      "weak galerkin finite element methods",
      "auto-stabilized weak galerkin finite element",
      "non-convex polytopal meshes",
      "stokes equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}