变系数三二次长方体有限元解最大模的超逼近

journal6 ›› 2010, Vol. 31 ›› Issue (3): 26-28.

变系数三二次长方体有限元解最大模的超逼近

（湖南涉外经济学院数学系，湖南长沙 410205）

出版日期:2010-05-25 发布日期:2012-04-17
作者简介:邓益军（1973- ），女，湖南邵东人，湖南涉外经济学院数学系讲师，硕士，主要从事偏微分方程数值解、有限元理论及应用的研究.
基金资助:
湖南省教育厅科学研究项目（07C576;03C212）

Maximum-Norm Superapproximation of the Triquadratic Block Finite Element Solution to the Three Dimension Problem with Variable Coefficients

(Department of Mathematics,Hunan International Economics College,Changsha 410205,China)

Online:2010-05-25 Published:2012-04-17

摘要/Abstract

摘要：针对某种三维变系数二阶椭圆方程，利用三维投影型插值算子和插值逼近性质获得了长方体剖分下三二次长方体有限元的弱估计，进而结合三维离散Green函数获得了高精度逐点意义下三二次长方体有限元位移及梯度最大模的超逼近.

关键词： 变系数椭圆方程, 长方体有限元, 投影型插值算子, 离散Green函数, 超逼近

Abstract: For an variable coefficients elliptic equation in 3D,weak estimates for the block finite element over rectangular parallelepiped partitions of the domain are obtained by using three- dimensional interpolation operator of projection type and interpolating approximation properties.Furthermore,in combination with three-dimensional discrete Green functions,the author derives the maximum-norm superapproximation results with high accuracy of the displacement and gradient for block finite elements.

Key words: variable coefficients elliptic equation, block finite element, interpolation operator of projection type, discrete Green funtions, superapproximation

邓益军. 变系数三二次长方体有限元解最大模的超逼近[J]. journal6, 2010, 31(3): 26-28.

DENG Yi-Jun. Maximum-Norm Superapproximation of the Triquadratic Block Finite Element Solution to the Three Dimension Problem with Variable Coefficients[J]. journal6, 2010, 31(3): 26-28.