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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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Analysis of recovery type a posteriori error estimators for mildly structured grids
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by Jinchao Xu and Zhimin Zhang HTML | PDF
Math. Comp. 73 (2004), 1139-1152 Request permission

Abstract:

Some recovery type error estimators for linear finite elements are analyzed under $O(h^{1+\alpha })$ $(\alpha > 0)$ regular grids. Superconvergence of order $O(h^{1+\rho })$ $(0 < \rho \le \alpha )$ is established for recovered gradients by three different methods. As a consequence, a posteriori error estimators based on those recovery methods are asymptotically exact.
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Additional Information
  • Jinchao Xu
  • Affiliation: Center for Computational Mathematics and Applications, Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
  • MR Author ID: 228866
  • Email: xu@math.psu.edu
  • Zhimin Zhang
  • Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
  • MR Author ID: 303173
  • Email: zzhang@math.wayne.edu
  • Received by editor(s): June 26, 2002
  • Received by editor(s) in revised form: December 15, 2002
  • Published electronically: August 19, 2003
  • Additional Notes: The work of the first author was supported in part by the National Science Foundation grant DMS-9706949 and the Center for Computational Mathematics and Applications, Penn State University
    The work of the second author was supported in part by the National Science Foundation grants DMS-0074301, DMS-0079743, and INT-0196139
  • © Copyright 2003 American Mathematical Society
  • Journal: Math. Comp. 73 (2004), 1139-1152
  • MSC (2000): Primary 65N30; Secondary 65N50, 65N15, 65N12, 65D10, 74S05, 41A10, 41A25
  • DOI: https://doi.org/10.1090/S0025-5718-03-01600-4
  • MathSciNet review: 2047081