{
  "id": "2004.06275",
  "version": "v1",
  "published": "2020-04-14T02:41:24.000Z",
  "updated": "2020-04-14T02:41:24.000Z",
  "title": "An interface/boundary-unfitted eXtended HDG method for linear elasticity problems",
  "authors": [
    "Yihui Han",
    "Xiao-Ping Wang",
    "Xiaoping Xie"
  ],
  "comment": "19 pages, 14 figures. arXiv admin note: text overlap with arXiv:1910.09769",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "An interface/boundary-unfitted eXtended hybridizable discontinuous Galerkin (X-HDG) method of arbitrary order is proposed for linear elasticity interface problems on unfitted meshes with respect to the interface and domain boundary. The method uses piecewise polynomials of degrees $k\\ (>= 1)$ and $k-1$ respectively for the displacement and stress approximations in the interior of elements inside the subdomains separated by the interface, and piecewise polynomials of degree $k$ for the numerical traces of the displacement on the inter-element boundaries inside the subdomains and on the interface/boundary of the domain. Optimal error estimates in $L^2$-norm for the stress and displacement are derived, which are uniform with respect to the Lam\\'e constant $\\lambda$. Finally, numerical experiments confirm the theoretical results and show that the method also applies to the case of crack-tip domain.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-14T02:41:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "interface/boundary-unfitted extended hdg method",
      "linear elasticity problems",
      "extended hybridizable discontinuous galerkin",
      "linear elasticity interface problems",
      "optimal error estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}