{
  "id": "1408.6037",
  "version": "v1",
  "published": "2014-08-26T07:35:48.000Z",
  "updated": "2014-08-26T07:35:48.000Z",
  "title": "A Posteriori Error Analysis of $hp$-FEM for singularly perturbed problems",
  "authors": [
    "Jens M. Melenk",
    "Thomas P. Wihler"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We consider the approximation of singularly perturbed linear second-order boundary value problems by $hp$-finite element methods. In particular, we include the case where the associated differential operator may not be coercive. Within this setting we derive an a posteriori error estimate for a natural residual norm. The error bound is robust with respect to the perturbation parameter and fully explicit with respect to both the local mesh size $h$ and the polynomial degree $p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-26T07:35:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30"
    ],
    "keywords": [
      "posteriori error analysis",
      "singularly perturbed problems",
      "linear second-order boundary value problems",
      "perturbed linear second-order boundary value"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.6037M"
    }
  }
}