Superconvergence of a Chebyshev Spectral Collocation Method

Authors:
Zhimin Zhang
Affiliations:
College of Mathematics and Computer Science, Hunan Normal University, Changsha, China 410081 and Department of Mathematics, Wayne State University, Detroit, USA 48202
Venue:
Journal of Scientific Computing
Year:
2008

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Superconvergence of the h-p version of the finite element method in one dimension

Journal of Computational and Applied Mathematics

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Abstract

We reveal the relationship between a Petrov---Galerkin method and a spectral collocation method at the Chebyshev points of the second kind (卤1 and zeros of U k ) for the two-point boundary value problem. Derivative superconvergence points are identified as the Chebyshev points of the first kind (Zeros of T k ). Super-geometric convergent rate is established for a special class of solutions.