{
  "id": "2105.06173",
  "version": "v1",
  "published": "2021-05-13T10:04:19.000Z",
  "updated": "2021-05-13T10:04:19.000Z",
  "title": "Mortar coupling of $hp$-discontinuous Galerkin and boundary element methods for the Helmholtz equation",
  "authors": [
    "Christoph Erath",
    "Lorenzo Mascotto",
    "Jens Markus Melenk",
    "Ilaria Perugia",
    "Alexander Rieder"
  ],
  "journal": "J.~Sci.~Comp. 92:1 (2022), paper nr. 2",
  "doi": "10.1007/s10915-022-01849-0",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We design and analyze a coupling of a discontinuous Galerkin finite element method with a boundary element method to solve the Helmholtz equation with variable coefficients in three dimensions. The coupling is realized with a mortar variable that is related to an impedance trace on a smooth interface. The method obtained has a block structure with nonsingular subblocks. We prove quasi-optimality of the $h$- and $p$-versions of the scheme, under a threshold condition on the approximability properties of the discrete spaces. Amongst others, an essential tool in the analysis is a novel discontinuous-to-continuous reconstruction operator on tetrahedral meshes with curved faces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-13T10:04:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N38",
      "65N12",
      "65N15",
      "35J05",
      "65R20"
    ],
    "keywords": [
      "boundary element method",
      "helmholtz equation",
      "mortar coupling",
      "discontinuous galerkin finite element method",
      "novel discontinuous-to-continuous reconstruction operator"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}