华东师范大学学报(自然科学版) ›› 2011, Vol. 2011 ›› Issue (4): 135-141.

• 数学 • 上一篇    

四维张量积二次矩形有限元最大模的超逼近

邓益军   

  1. 湖南涉外经济学院 数学系, 长沙 410205
  • 收稿日期:2010-11-01 修回日期:2011-02-01 出版日期:2011-07-05 发布日期:2011-11-12

Maximum-norm superapproximations for tensor-product quadratic rectangular finite elements in 4D

DENG Yi-jun   

  1. Department of Mathematics, Hunan International Economics University, Changsha 410205, China
  • Received:2010-11-01 Revised:2011-02-01 Online:2011-07-05 Published:2011-11-12

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摘要： 针对Poisson方程Dirichlet边值问题, 首先建立了四维投影型插值算子, 并应用它得到了正规剖分下四维张量积二次矩形有限元的弱估计. 在此基础上, 结合四维离散Green函数的估计, 研究四维张量积二次矩形有限元解及梯度最大模的超逼近, 获得了逐点意义下高精度的超收敛结果.

关键词: 椭圆边值问题, 四维投影型插值算子, 矩形有限元, 弱估计, 超逼近

Abstract: For Dirichlet boundary value problems of Poisson equations, an interpolation operator of projection type in 4D was established. Then by using this operator, weak estimates for tensor-product quadratic rectangular finite elements over regular partitions of a domain were obtained. Based on the obtained results and the estimates for the four-dimensional discrete Green's function, some highly accuracy results of the maximum-norm superapproximations of finite elements were derived.

Key words: elliptic boundary value problem, interpolation operator of projection type in 4D, rectangular finite element, weak estimate, superapproximation

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