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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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Superconvergence of quadratic finite elements on mildly structured grids
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by Yunqing Huang and Jinchao Xu PDF
Math. Comp. 77 (2008), 1253-1268 Request permission

Abstract:

Superconvergence estimates are studied in this paper on quadratic finite element discretizations for second order elliptic boundary value problems on mildly structured triangular meshes. For a large class of practically useful grids, the finite element solution $u_h$ is proven to be superclose to the interpolant $u_I$ and as a result a postprocessing gradient recovery scheme for $u_h$ can be devised. The analysis is based on a number of carefully derived identities. In addition to its own theoretical interests, the result in this paper can be used for deriving asymptotically exact a posteriori error estimators for quadratic finite element methods.
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Additional Information
  • Yunqing Huang
  • Affiliation: Institute for Computational and Applied Mathematics and Hunan Key Laboratory for Computation & Simulation in Science & Engineering, Xiangtan University, People’s Republic of China, 411105
  • Email: huangyq@xtu.edu.cn
  • Jinchao Xu
  • Affiliation: Institute for Computational and Applied Mathematics, Xiangtan University, People’s Republic of China and Center for Computational Mathematics and Applications, Pennsylvania State University, USA
  • MR Author ID: 228866
  • Email: xu@math.psu.edu
  • Received by editor(s): February 2, 2006
  • Received by editor(s) in revised form: March 2, 2007
  • Published electronically: March 4, 2008
  • Additional Notes: The work of the first author was supported in part by the NSFC for Distinguished Young Scholars (10625106) and the National Basic Research Program of China under the grant 2005CB321701
    The second author was supported in part by the Furong Scholar Program of Hunan Province through Xiangtan University
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 77 (2008), 1253-1268
  • MSC (2000): Primary 65N50, 65N30
  • DOI: https://doi.org/10.1090/S0025-5718-08-02051-6
  • MathSciNet review: 2398767