{
  "id": "1406.3108",
  "version": "v2",
  "published": "2014-06-12T03:18:37.000Z",
  "updated": "2014-09-27T18:53:17.000Z",
  "title": "Hessian Recovery for Finite Element Methods",
  "authors": [
    "Hailong Guo",
    "Zhimin Zhang",
    "Ren Zhao"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "In this article, we propose and analyze an effective Hessian recovery strategy for the Lagrangian finite element of arbitrary order $k$. We prove that the proposed Hessian recovery preserves polynomials of degree $k+1$ on general unstructured meshes and superconverges at rate $O(h^k)$ on mildly structured meshes. In addition, the method preserves polynomials of degree $k+2$ on translation invariant meshes and produces a symmetric Hessian matrix when the sampling points for recovery are selected with symmetry. Numerical examples are presented to support our theoretical results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-12T03:18:37.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-27T18:53:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite element methods",
      "hessian recovery preserves polynomials",
      "method preserves polynomials",
      "lagrangian finite element",
      "symmetric hessian matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.3108G"
    }
  }
}