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Derivative superconvergent points in finite element solutions of harmonic functions-- A theoretical justification

Author: Zhimin Zhang
Journal: Math. Comp. 71 (2002), 1421-1430
MSC (2000): Primary 65N30
Published electronically: December 5, 2001
MathSciNet review: 1933038
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Abstract: Finite element derivative superconvergent points for harmonic functions under local rectangular mesh are investigated. All superconvergent points for the finite element space of any order that is contained in the tensor-product space and contains the intermediate family can be predicted. In the case of the serendipity family, results are given for finite element spaces of order below 6. The results justify the computer findings of Babuska, et al.

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Additional Information

Zhimin Zhang
Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202

Keywords: Superconvergence, finite element, harmonic function
Received by editor(s): November 21, 2000
Published electronically: December 5, 2001
Article copyright: © Copyright 2001 American Mathematical Society