{
  "id": "2401.04485",
  "version": "v1",
  "published": "2024-01-09T10:51:47.000Z",
  "updated": "2024-01-09T10:51:47.000Z",
  "title": "On the stabilization of a virtual element method for an acoustic vibration problem",
  "authors": [
    "Linda Alzaben",
    "Daniele Boffi",
    "Andreas Dedner",
    "Lucia Gastaldi"
  ],
  "comment": "36 pages, 7 figures, 14 tables",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In this paper we introduce an abstract setting for the convergence analysis of the virtual element approximation of an acoustic vibration problem. We discuss the effect of the stabilization parameters and remark that in some cases it is possible to achieve optimal convergence without the need of any stabilization. This statement is rigorously proved for lowest order triangular element and supported by several numerical experiments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-09T10:51:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N25",
      "65N30",
      "70J30",
      "76M10"
    ],
    "keywords": [
      "acoustic vibration problem",
      "virtual element method",
      "stabilization",
      "lowest order triangular element",
      "virtual element approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}