{
  "id": "1301.6860",
  "version": "v2",
  "published": "2013-01-29T08:11:27.000Z",
  "updated": "2013-10-04T05:22:35.000Z",
  "title": "Convergence analysis of a family of 14-node brick elements",
  "authors": [
    "Zhaoliang Meng",
    "Zhongxuan Luo",
    "Dongwoo Sheen",
    "Sihwan Kim"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "In this paper, we will give convergence analysis for a family of 14-node elements which was proposed by I. M. Smith and D. J. Kidger in 1992. The 14 DOFs are taken as the value at the eight vertices and six face-centroids. For second-order elliptic problem, we will show that among all the Smith-Kidger 14-node elements, Type 1, Type 2 and type 5 elements can get the optimal convergence order and Type 6 get lower convergence order. Motivated by the proof, we also present a new 14-node nonconforming element. If we change the DOFs into the value at the eight vertices and the integration value of six faces, we show that Type 1, Type 2 and Type 5 keep the optimal convergence order and Type 6 element improve one order accuracy which means that it also get optimal convergence order.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-10-04T05:22:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convergence analysis",
      "optimal convergence order",
      "brick elements",
      "lower convergence order",
      "second-order elliptic problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.6860M"
    }
  }
}