Anisotropic conforming rectangular elements for elliptic problems of any order

Authors:
Shaochun Chen;Yongqin Yang;Shipeng Mao
Affiliations:
Department of Mathematics, Zhengzhou University, 450052, China;Department of Mathematics, Zhengzhou University, 450052, China;Institute of Computational Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, PO Box 2719, Beijing, 100080, China
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

In this paper two sets of C^N^-^1 conforming rectangular elements for linear elliptic problems of order 2N, N=1, are presented. One is b"i-(2N-1) element, well known b"i-linear element and b"i-cubic C^1 element (Bogner-Fox-Schmit) correspond to N=1 and N=2, respectively. Another one is b"i-2N element, well known b"i-quadratic element corresponds to N=1. The anisotropic error estimates are proved by the Newton's formulas for Hermite interpolation in two dimension and the special properties of the divided differences with coincident knots presented in this paper.