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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Hessian recovery for finite element methods
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by Hailong Guo, Zhimin Zhang and Ren Zhao PDF
Math. Comp. 86 (2017), 1671-1692 Request permission

Abstract:

In this article, we propose and analyze an effective Hessian recovery strategy for the Lagrangian finite element method of arbitrary order. We prove that the proposed Hessian recovery method preserves polynomials of degree $k+1$ on general unstructured meshes and superconverges at a rate of $O(h^k)$ on mildly structured meshes. In addition, the method is proved to be ultraconvergent (two orders higher) for the translation invariant finite element space of any order. Numerical examples are presented to support our theoretical results.
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Additional Information
  • Hailong Guo
  • Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
  • Address at time of publication: Department of Mathematics, University of California, Santa Barbara, California 93106
  • MR Author ID: 1022936
  • Email: hlguo@math.ucsb.edu
  • Zhimin Zhang
  • Affiliation: Beijing Computational Science Research Center, Beijing 100193, China – and – Department of Mathematics, Wayne State University, Detroit, Michigan 48202
  • Email: zmzhang@csrc.ac.cn, zzhang@math.wayne.edu
  • Ren Zhao
  • Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
  • MR Author ID: 1142013
  • Email: rzhao@math.wayne.edu
  • Received by editor(s): July 17, 2014
  • Received by editor(s) in revised form: December 14, 2015
  • Published electronically: September 27, 2016
  • Additional Notes: The second author is the corresponding author. The research of the second author was supported in part by the National Natural Science Foundation of China under grants 11471031, 91430216 U1530401, and the U.S. National Science Foundation through grant DMS-1419040.
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 1671-1692
  • MSC (2010): Primary 65N50, 65N30; Secondary 65N15
  • DOI: https://doi.org/10.1090/mcom/3186
  • MathSciNet review: 3626532