{
  "id": "1712.09267",
  "version": "v1",
  "published": "2017-12-26T13:51:24.000Z",
  "updated": "2017-12-26T13:51:24.000Z",
  "title": "A saturation property for the spectral-Galerkin approximation of a Dirichlet problem in a square",
  "authors": [
    "Claudio Canuto",
    "Ricardo H. Nochetto",
    "Rob Stevenson",
    "Marco Verani"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "Both practice and analysis of adaptive $p$-FEMs and $hp$-FEMs raise the question what increment in the current polynomial degree $p$ guarantees a $p$-independent reduction of the Galerkin error. We answer this question for the $p$-FEM in the simplified context of homogeneous Dirichlet problems for the Poisson equation in the two dimensional unit square with polynomial data of degree $p$. We show that an increment proportional to $p$ yields a $p$-robust error reduction and provide computational evidence that a constant increment does not.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-26T13:51:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirichlet problem",
      "spectral-galerkin approximation",
      "saturation property",
      "current polynomial degree",
      "robust error reduction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}