{
  "id": "2205.13301",
  "version": "v1",
  "published": "2022-05-26T12:23:23.000Z",
  "updated": "2022-05-26T12:23:23.000Z",
  "title": "A DPG method for Reissner-Mindlin plates",
  "authors": [
    "Thomas Führer",
    "Norbert Heuer",
    "Antti H. Niemi"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We present a discontinuous Petrov-Galerkin (DPG) method with optimal test functions for the Reissner-Mindlin plate bending model. Our method is based on a variational formulation that utilizes a Helmholtz decomposition of the shear force. It produces approximations of the primitive variables and the bending moments. For any canonical selection of boundary conditions the method converges quasi-optimally. In the case of hard-clamped convex plates, we prove that the lowest-order scheme is locking free. Several numerical experiments confirm our results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-26T12:23:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "74S05",
      "35J35",
      "65N30",
      "35J67",
      "74K20"
    ],
    "keywords": [
      "dpg method",
      "optimal test functions",
      "reissner-mindlin plate bending model",
      "variational formulation",
      "shear force"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}