{
  "id": "0803.3824",
  "version": "v1",
  "published": "2008-03-27T12:05:44.000Z",
  "updated": "2008-03-27T12:05:44.000Z",
  "title": "Convergence rates for adaptive finite elements",
  "authors": [
    "Fernando D. Gaspoz",
    "Pedro Morin"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "In this article we prove that it is possible to construct, using newest-vertex bisection, meshes that equidistribute the error in $H^1$-norm, whenever the function to approximate can be decomposed as a sum of a regular part plus a singular part with singularities around a finite number of points. This decomposition is usual in regularity results of Partial Differential Equations (PDE). As a consequence, the meshes turn out to be quasi-optimal, and convergence rates for adaptive finite element methods (AFEM) using Lagrange finite elements of any polynomial degree are obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-27T12:05:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convergence rates",
      "lagrange finite elements",
      "adaptive finite element methods",
      "regular part plus",
      "partial differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.3824G"
    }
  }
}