{
  "id": "2209.00957",
  "version": "v1",
  "published": "2022-09-02T11:33:56.000Z",
  "updated": "2022-09-02T11:33:56.000Z",
  "title": "Cohomology of the discrete de Rham complex on domains of general topology",
  "authors": [
    "Daniele A. Di Pietro",
    "Jérôme Droniou",
    "Silvano Pitassi"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In this work we prove that, for a general polyhedral domain of $\\Real^3$, the cohomology spaces of the discrete de Rham complex of [Di Pietro and Droniou, An arbitrary-order discrete de Rham complex on polyhedral meshes: Exactness, Poincar\\'e inequalities, and consistency, Found. Comput. Math., 2021, DOI: \\href{https://dx.doi.org/10.1007/s10208-021-09542-8}{10.1007/s10208-021-09542-8}] are isomorphic to those of the continuous de Rham complex. This is, to the best of our knowledge, the first result of this kind for an arbitrary-order complex built from a general polyhedral mesh.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-02T11:33:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "65N99",
      "65N12"
    ],
    "keywords": [
      "rham complex",
      "general topology",
      "general polyhedral domain",
      "general polyhedral mesh",
      "arbitrary-order complex built"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}