{
  "id": "2007.04147",
  "version": "v1",
  "published": "2020-07-08T14:19:48.000Z",
  "updated": "2020-07-08T14:19:48.000Z",
  "title": "Error estimates of hybridizable interior penalty methods using a variable penalty for highly anisotropic diffusion problems",
  "authors": [
    "Gregory Etangsale",
    "Marwan Fahs",
    "Vincent Fontaine",
    "Nalitiana Rajaonison"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In this paper, we derive improved a priori error estimates for families of hybridizable interior penalty discontinuous Galerkin (H-IP) methods using a variable penalty for second-order elliptic problems. The strategy is to use a penalization function of the form $\\mathcal{O}(1/h^{1+\\delta})$, where $h$ denotes the mesh size and $\\delta$ is a user-dependent parameter. We then quantify its direct impact on the convergence analysis, namely, the (strong) consistency, discrete coercivity and boundedness (with $h^{\\delta}$-dependency), and we derive updated error estimates for both discrete energy- and $L^{2}$-norms. All theoretical results are supported by numerical evidence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-08T14:19:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N12",
      "65N15",
      "65N30",
      "65N38"
    ],
    "keywords": [
      "hybridizable interior penalty methods",
      "highly anisotropic diffusion problems",
      "error estimates",
      "variable penalty",
      "interior penalty discontinuous galerkin"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}