{
  "id": "1306.5115",
  "version": "v1",
  "published": "2013-06-21T12:25:42.000Z",
  "updated": "2013-06-21T12:25:42.000Z",
  "title": "Each H^{1/2}-stable projection yields convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data in R^d",
  "authors": [
    "Markus Aurada",
    "Michael Feischl",
    "Josef Kemetmüller",
    "Marcus Page",
    "Dirk Praetorius"
  ],
  "comment": "37 pages, 8 figures",
  "journal": "M2AN Math. Model. Numer. Anal., 47 (2013), 1207-1235",
  "doi": "10.1051/m2an/2013069",
  "categories": [
    "math.NA"
  ],
  "abstract": "We consider the solution of second order elliptic PDEs in $\\R^d$ with inhomogeneous Dirichlet data by means of an $h$-adaptive FEM with fixed polynomial order $p\\in\\N$. As model example serves the Poisson equation with mixed Dirichlet-Neumann boundary conditions, where the inhomogeneous Dirichlet data are discretized by use of an $H^{1/2}$-stable projection, for instance, the $L^2$-projection for $p=1$ or the Scott-Zhang projection for general $p\\ge1$. For error estimation, we use a residual error estimator which includes the Dirichlet data oscillations. We prove that each $H^{1/2}$-stable projection yields convergence of the adaptive algorithm even with quasi-optimal convergence rate. Numerical experiments with the $L^2$- and Scott-Zhang projection conclude the work.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-21T12:25:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "65N50"
    ],
    "keywords": [
      "inhomogeneous dirichlet data",
      "adaptive fem",
      "second order elliptic pdes",
      "quasi-optimality",
      "quasi-optimal convergence rate"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.5115A"
    }
  }
}