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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 spectral collocation and $p$-version methods in one dimensional problems
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by Zhimin Zhang PDF
Math. Comp. 74 (2005), 1621-1636 Request permission


Superconvergence phenomenon of the Legendre spectral collocation method and the $p$-version finite element method is discussed under the one dimensional setting. For a class of functions that satisfy a regularity condition (M): $\|u^{(k)}\|_{L^\infty }\le cM^k$ on a bounded domain, it is demonstrated, both theoretically and numerically, that the optimal convergent rate is supergeometric. Furthermore, at proper Gaussian points or Lobatto points, the rate of convergence may gain one or two orders of the polynomial degree.
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Additional Information
  • Zhimin Zhang
  • Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
  • MR Author ID: 303173
  • Email:
  • Received by editor(s): April 28, 2004
  • Received by editor(s) in revised form: July 16, 2004
  • Published electronically: March 18, 2005
  • Additional Notes: This work was supported in part by the National Science Foundation grants DMS-0074301 and DMS-0311807
  • © Copyright 2005 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 1621-1636
  • MSC (2000): Primary 65N30, 65N15
  • DOI:
  • MathSciNet review: 2164089