{
  "id": "1811.09194",
  "version": "v1",
  "published": "2018-11-22T14:36:33.000Z",
  "updated": "2018-11-22T14:36:33.000Z",
  "title": "An embedded--hybridized discontinuous Galerkin finite element method for the Stokes equations",
  "authors": [
    "Sander Rhebergen",
    "Garth N. Wells"
  ],
  "categories": [
    "math.NA",
    "cs.CE",
    "cs.NA"
  ],
  "abstract": "We present and analyze a new embedded--hybridized discontinuous Galerkin finite element method for the Stokes problem. The method has the attractive properties of full hybridized methods, namely a $H({\\rm div})$-conforming velocity field, pointwise satisfaction of the continuity equation and \\emph{a priori} error estimates for the velocity that are independent of the pressure. The embedded--hybridized formulation has advantages over a full hybridized formulation in that it has fewer global degrees-of-freedom for a given mesh and the algebraic structure of the resulting linear system is better suited to fast iterative solvers. The analysis results are supported by a range of numerical examples that demonstrate rates of convergence, and which show substantial computational efficiency gains over a full hybridized formulation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-22T14:36:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65F08",
      "65M15",
      "65N12",
      "65N30",
      "76D07"
    ],
    "keywords": [
      "discontinuous galerkin finite element method",
      "embedded-hybridized discontinuous galerkin finite element",
      "stokes equations",
      "full hybridized formulation",
      "substantial computational efficiency gains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}