{
  "id": "2204.09955",
  "version": "v1",
  "published": "2022-04-21T08:24:50.000Z",
  "updated": "2022-04-21T08:24:50.000Z",
  "title": "Interior estimates for the Virtual Element Method",
  "authors": [
    "Silvia Bertoluzza",
    "Micol Pennacchio",
    "Daniele Prada"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We analyze the local accuracy of the virtual element method. More precisely, we prove an error bound similar to the one holding for the finite element method, namely, that the local $H^1$ error in a interior subdomain is bounded by a term behaving like the best approximation allowed by the local smoothness of the solution in a larger interior subdomain plus the global error measured in a negative norm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-21T08:24:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "65N12"
    ],
    "keywords": [
      "virtual element method",
      "interior estimates",
      "larger interior subdomain plus",
      "finite element method",
      "error bound similar"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}