Anisotropic conforming rectangular elements for elliptic problems of any order

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• 作者：Shaochun Chen ; Yongqin Yang ; Shipeng Mao
• 关键词：Anisotropic Hermite interpolation ; Divided difference with coincident knots ; Elliptic problem of any order
• 刊名：Applied Numerical Mathematics
• 出版年：2009
• 出版时间：May 2009
• 年：2009
• 卷：59
• 期：5
• 页码：1137-1148
• 全文大小：172 K

文摘

In this paper two sets of C^N−1 conforming rectangular elements for linear elliptic problems of order 2N, N1, are presented. One is b_i−(2N−1) element, well known b_i-linear element and b_i-cubic C¹ 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.