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一个新的非常规Hermite型各向异性矩形元的超收敛分析及外推

石东洋,梁慧   

  1. 郑州大学数学系,郑州大学数学系 郑州 450002 ,郑州 450002 哈尔滨工业大学理学院,哈尔滨 150001
  • 出版日期:2005-04-14 发布日期:2005-04-14

石东洋,梁慧. 一个新的非常规Hermite型各向异性矩形元的超收敛分析及外推[J]. 计算数学, 2005, 27(4): 369-382.

SUPERCONVERGENCE ANALYSIS AND EXTRAPOLATION OF A NEW UNCONVENTIONAL HERMITE-TYPE ANISOTROPIC RECTANGULAR ELEMENT

  1. Shi Dongyang (Department of Mathematics, Zhengzhou University, Zhengzhou 450002, China) Liang Hui (Department of Mathematics, Zhengzhou University, Zhengzhou 450002, China; School of Science, Harbin Institute of Technology, Harbin 150001, China)
  • Online:2005-04-14 Published:2005-04-14

本文对二阶椭圆问题构造了一个新的非常规Hermite型矩形单元并用各向异性插值基本定理证明了其各向异性特征,从而可用于任意的矩形剖分.同时还得到了与网格的正则性假设和拟一致假设无关的超逼近和超收敛性质以及外推.数值结果表明该单元确实是一个具有很好应用价值的单元且与理论分析是相吻合的.

In this paper, a new unconventional Hermite-type rectangular element for the second order elliptic problem is constructed. The anisotropic character is proved by using anisotropic interpolate basic theorem, thus this element can be applied to arbitrary rectangular subdivision. At the same time, the superclose and super-convergence properties and extrapolation are obtained, which are independent of the regular assumption and quasi-uniform assumption of the meshes. Numerical results which coincide with our theoretical analysis show that this element indeed has very good convergence behavior.

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