{
  "id": "1608.04081",
  "version": "v1",
  "published": "2016-08-14T09:54:34.000Z",
  "updated": "2016-08-14T09:54:34.000Z",
  "title": "An analysis of a class of variational multiscale methods based on subspace decomposition",
  "authors": [
    "Ralf Kornhuber",
    "Harry Yserentant"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "Numerical homogenization tries to approximate the solutions of elliptic partial differential equations with strongly oscillating coefficients by functions from modified finite element spaces. We present in this paper a class of such methods that are very closely related to the method of M{\\aa}lqvist and Peterseim [Math. Comp. 83, 2014]. Like the method of M{\\aa}lqvist and Peterseim, these methods do not make explicit or implicit use of a scale separation. Their compared to that in the work of M{\\aa}lqvist and Peterseim strongly simplified analysis is based on a reformulation of their method in terms of variational multiscale methods and on the theory of iterative methods, more precisely, of additive Schwarz or subspace decomposition methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-14T09:54:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "65N55"
    ],
    "keywords": [
      "variational multiscale methods",
      "elliptic partial differential equations",
      "modified finite element spaces",
      "subspace decomposition methods",
      "peterseim strongly simplified analysis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}