{
  "id": "1207.3257",
  "version": "v2",
  "published": "2012-07-13T14:15:18.000Z",
  "updated": "2012-07-16T08:06:20.000Z",
  "title": "Convergence of adaptive FEM for some elliptic obstacle problem with inhomogeneous Dirichlet data",
  "authors": [
    "Michael Feischl",
    "Marcus Page",
    "Dirk Praetorius"
  ],
  "comment": "submitted to: International Journal of Numerical Analysis & Modeling",
  "journal": "Int. J. Numer. Anal. Model., 11 (2014), 229-253",
  "categories": [
    "math.NA"
  ],
  "abstract": "In this work, we show the convergence of adaptive lowest-order FEM (AFEM) for an elliptic obstacle problem with non-homogeneous Dirichlet data, where the obstacle \\chi\\ is restricted only by \\chi\\ in H^2(\\Omega). The adaptive loop is steered by some residual based error estimator introduced in Braess, Carstensen & Hoppe (2007) that is extended to control oscillations of the Dirichlet data, as well. In the spirit of Cascon et al. (2008), we show that a weighted sum of energy error, estimator, and Dirichlet oscillations satisfies a contraction property up to certain vanishing energy contributions. This result extends the analysis of Braess, Carstensen & Hoppe (2007) and Page & Praetorius (2010) to the case of non-homogeneous Dirichlet data as well as certain non-affine obstacles and introduces some energy estimates to overcome the lack of nestedness of the discrete spaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-07-16T08:06:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "65N50"
    ],
    "keywords": [
      "elliptic obstacle problem",
      "inhomogeneous dirichlet data",
      "adaptive fem",
      "convergence",
      "non-homogeneous dirichlet data"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.3257F"
    }
  }
}