{
  "id": "2012.15582",
  "version": "v1",
  "published": "2020-12-31T12:36:16.000Z",
  "updated": "2020-12-31T12:36:16.000Z",
  "title": "Isogeometric discretizations of the Stokes problem on trimmed geometries",
  "authors": [
    "Riccardo Puppi"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "The isogeometric approximation of the Stokes problem in a trimmed domain is studied. This setting is characterized by an underlying mesh unfitted with the boundary of the physical domain making the imposition of the essential boundary conditions a challenging problem. A very popular strategy is to rely on the so-called Nitsche method [22]. We show with numerically examples that in some degenerate trimmed domain configurations there is a lack of stability of the formulation, potentially polluting the computed solutions. After extending the stabilization procedure of [17] to incompressible flow problems, we theoretically prove that, combined with the Raviart-Thomas isogeometric element, we are able to recover the well-posedness of the formulation and, consequently, optimal a priori error estimates. Numerical results corroborating the theory and extending it for the case of the isogeometric N\\'ed\\'elec and Taylor-Hood elements are provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-31T12:36:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stokes problem",
      "isogeometric discretizations",
      "trimmed geometries",
      "priori error estimates",
      "essential boundary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}