{
  "id": "2012.03425",
  "version": "v1",
  "published": "2020-12-07T02:47:11.000Z",
  "updated": "2020-12-07T02:47:11.000Z",
  "title": "Multipatch Discontinuous Galerkin IGA for the Biharmonic Problem On Surfaces",
  "authors": [
    "Stephen E. Moore"
  ],
  "comment": "20 pages; 7 figures",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We present the analysis of interior penalty discontinuous Galerkin Isogeometric Analysis (dGIGA) for the biharmonic problem on orientable surfaces $\\Omega \\subset \\mathbb{R}^3.$ Here, we consider a surface consisting of several non-overlapping patches as typical in multipatch dGIGA. Due to the non-overlapping nature of the patches, we construct NURBS approximation spaces which are discontinuous across the patch interfaces via a penalty scheme. By an appropriate discrete norm, we present \\textit{a priori} error estimates for the non-symmetric, symmetric and semi-symmetric interior penalty methods. Finally, we confirm our theoritical results with numerical experiments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-07T02:47:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N30",
      "65N22",
      "65N15",
      "G.1.0",
      "G.1.3",
      "G.1.8"
    ],
    "keywords": [
      "multipatch discontinuous galerkin iga",
      "biharmonic problem",
      "penalty discontinuous galerkin isogeometric analysis",
      "interior penalty discontinuous galerkin isogeometric",
      "semi-symmetric interior penalty methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}