椭圆型方程四面体线元的超逼近与外推  

Superclose and Extrapolation of the Tetrahedral Linear Finite Elements for Elliptic Problem

作　　者：林群[1] 周俊明[2] 陈焘 

机构地区：[1]中国科学院数学与系统科学研究院,北京100190 [2]河北工业大学理学院,天津300130

出　　处：《数学的实践与认识》2009年第15期200-208,共9页Mathematics in Practice and Theory

摘　　要：重新讨论了三角线元的积分恒等式,使之适用于三维区域的拟一致四面体元,借此证明了椭圆型方程有限元解梯度有超逼近现象,函数值Richardson外推可以提高精度.The integral identities of triangular linear elements are improved, so they also apply to quasi-uniform tetrahedral linear elements. Then the authors show that the tetrahedral linear finite element solution uh and the tetrahedral linear interpolation ul have superclose gradient for elliptic problem and obtain the improved accuracy through Richardson extrapolation of the tetrahedral linear finite element solution uh.

关 键 词：四面体线元 积分恒等式 超逼近 外推 

分 类 号：O175.25[理学—数学] TN011[理学—基础数学]