{
  "id": "2408.11927",
  "version": "v1",
  "published": "2024-08-21T18:31:01.000Z",
  "updated": "2024-08-21T18:31:01.000Z",
  "title": "Auto-Stabilized Weak Galerkin Finite Element Methods on Polytopal Meshes without Convexity Constraints",
  "authors": [
    "Chunmei Wang"
  ],
  "comment": "19 pages",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "This paper introduces an auto-stabilized weak Galerkin (WG) finite element method with a built-in stabilizer for Poisson equations. By utilizing bubble functions as a key analytical tool, our method extends to both convex and non-convex elements in finite element partitions, marking a significant advancement over existing stabilizer-free WG methods. It overcomes the restrictive conditions of previous approaches and is applicable in any dimension $d$, offering substantial advantages. The proposed method maintains a simple, symmetric, and positive definite structure. These benefits are evidenced by optimal order error estimates in both discrete $H^1$ and $L^2$ norms, highlighting the effectiveness and accuracy of our WG method for practical applications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-21T18:31:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "65N15",
      "65N12",
      "65N20"
    ],
    "keywords": [
      "weak galerkin finite element methods",
      "auto-stabilized weak galerkin finite element",
      "convexity constraints",
      "polytopal meshes",
      "wg method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}