{
  "id": "1408.5545",
  "version": "v1",
  "published": "2014-08-24T03:07:37.000Z",
  "updated": "2014-08-24T03:07:37.000Z",
  "title": "Analysis of a family of HDG methods for second order elliptic problems",
  "authors": [
    "Binjie Li",
    "Xiaoping Xie"
  ],
  "comment": "25 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "In this paper, we propose and analyze a new family of hybridizable discontinuous Galerkin (HDG) methods for second order elliptic problems in two and three dimensions. We use piecewise polynomials of degree $k\\geqslant 0$ for both the flux and numerical trace, and piecewise polynomials of degree $k+1$ for the potential. We show the convergence orders of the flux and the potential in $L^2$-norm are $k+1$ and $k+2$, respectively. What's more, we construct a local postprocessing for the flux, which produces a numerical flux with better conservation. We also study the conditioning of the HDG method. We finally do numerical experiments in two-space dimensions to verify our theoretical results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-24T03:07:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N12",
      "65N30"
    ],
    "keywords": [
      "second order elliptic problems",
      "hdg method",
      "piecewise polynomials",
      "convergence orders",
      "better conservation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.5545L"
    }
  }
}