{
  "id": "1906.04869",
  "version": "v1",
  "published": "2019-06-12T00:17:18.000Z",
  "updated": "2019-06-12T00:17:18.000Z",
  "title": "An ultraweak formulation of the Reissner-Mindlin plate bending model and DPG approximation",
  "authors": [
    "Thomas Führer",
    "Norbert Heuer",
    "Francisco-Javier Sayas"
  ],
  "comment": "31 pages, 1 figure",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We develop and analyze an ultraweak variational formulation of the Reissner-Mindlin plate bending model both for the clamped and the soft simply supported cases. We prove well-posedness of the formulation, uniformly with respect to the plate thickness $t$. We also prove weak convergence of the Reissner-Mindlin solution to the solution of the corresponding Kirchhoff-Love model when $t\\to 0$. Based on the ultraweak formulation, we introduce a discretization of the discontinuous Petrov-Galerkin type with optimal test functions (DPG) and prove its uniform quasi-optimal convergence. Our theory covers the case of non-convex polygonal plates. A numerical experiment for some smooth model solutions with fixed load confirms that our scheme is locking free.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-12T00:17:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "74S05",
      "74K20",
      "35J35",
      "65N30",
      "35J67"
    ],
    "keywords": [
      "reissner-mindlin plate bending model",
      "ultraweak formulation",
      "dpg approximation",
      "ultraweak variational formulation",
      "optimal test functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}