{
  "id": "1609.04437",
  "version": "v1",
  "published": "2016-09-14T20:35:06.000Z",
  "updated": "2016-09-14T20:35:06.000Z",
  "title": "Robust recovery-type a posteriori error estimators for streamline upwind/Petrov Galerkin discretizations for singularly perturbed problems",
  "authors": [
    "Shaohong Du",
    "Runchang Lin",
    "Zhimin Zhang"
  ],
  "comment": "20 pages, 14 figures",
  "categories": [
    "math.NA"
  ],
  "abstract": "In this paper, we investigate adaptive streamline upwind/Petrov Galerkin (SUPG) methods for singularly perturbed convection-diffusion-reaction equations in a new dual norm presented in [Du and Zhang, J. Sci. Comput. (2015)]. The flux is recovered by either local averaging in conforming $H({\\rm div})$ spaces or weighted global $L^2$ projection onto conforming $H({\\rm div})$ spaces. We further introduce a recovery stabilization procedure, and develop completely robust a posteriori error estimators with respect to the singular perturbation parameter $\\varepsilon$. Numerical experiments are reported to support the theoretical results and to show that the estimated errors depend on the degrees of freedom uniformly in $\\varepsilon$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-14T20:35:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N15",
      "65N30",
      "65J15"
    ],
    "keywords": [
      "streamline upwind/petrov galerkin discretizations",
      "posteriori error estimators",
      "singularly perturbed problems",
      "robust recovery-type",
      "adaptive streamline upwind/petrov galerkin"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}