{
  "id": "1902.09829",
  "version": "v1",
  "published": "2019-02-26T09:51:59.000Z",
  "updated": "2019-02-26T09:51:59.000Z",
  "title": "Error estimates in balanced norms of finite element methods for higher order reaction-diffusion problems",
  "authors": [
    "Sebastian Franz",
    "Hans-G. Roos"
  ],
  "comment": "13 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "Error estimates of finite element methods for reaction-diffusion problems are often realised in the related energy norm. In the singularly perturbed case, however, this norm is not adequate. A different scaling of the $H^m$ seminorm for $2m$-th order problems leads to a balanced norm which reflects the layer behaviour correctly. We prove error estimates in such balanced norms and improve thereby existing estimates known in literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-26T09:51:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N12",
      "65N15",
      "65N30"
    ],
    "keywords": [
      "higher order reaction-diffusion problems",
      "finite element methods",
      "error estimates",
      "balanced norm",
      "th order problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}