{
  "id": "2212.01720",
  "version": "v1",
  "published": "2022-12-04T01:42:52.000Z",
  "updated": "2022-12-04T01:42:52.000Z",
  "title": "Stabilization-Free Virtual Element Methods",
  "authors": [
    "Chunyu Chen",
    "Xuehai Huang",
    "Huayi Wei"
  ],
  "comment": "20 pages",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "Stabilization-free virtual element methods in arbitrary degree of polynomial are developed for second order elliptic problems, including a nonconforming virtual element method in arbitrary dimension and a conforming virtual element method in two dimensions. The key is to construct local $H(\\textrm{div})$-conforming macro finite element spaces such that the associated $L^2$ projection of the gradient of virtual element functions is computable, and the $L^2$ projector has a uniform lower bound on the gradient of virtual element function spaces in $L^2$ norm. Optimal error estimates are derived for these stabilization-free virtual element methods. Numerical results are provided to verify the convergence rates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-04T01:42:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N12",
      "65N22",
      "65N30"
    ],
    "keywords": [
      "stabilization-free virtual element methods",
      "second order elliptic problems",
      "virtual element function spaces",
      "conforming macro finite element spaces",
      "nonconforming virtual element method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}