解两点边值问题的基于应力佳点的二次有限体积元法  

Quadratic Finite Volume Element Method Based on Optimal Stress Points for Solving Two-point Boundary Value Problems

作　　者：于长华[1] 李永海[2] 

机构地区：[1]吉林大学数学研究所,长春130012 [2]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2009年第4期639-648,共10页Journal of Jilin University:Science Edition

基　　金：吉林大学"985工程"项目基金

摘　　要：构造了求解两点边值问题的一种新的Lagrange型二次有限体积元法,取应力佳点(Gauss点)作为对偶单元的节点,试探函数空间取Lagrange型二次有限元空间、检验函数空间取相应于对偶剖分的分片常数函数空间.证明了新方法具有最优的H1模和L2模误差估计,讨论了在应力佳点导数的超收敛估计,并通过数值实验验证了理论分析结果.In this paper, a new kind of Lagrangian quadratic finite volume element method based on optimal stress points is presented for solving two-point boundary value problems, In general, trial and test spaces are chosen as the Lagrangian quadratic finite element space and the piecewise constant function space respectively. It is proved that the method has optimal H1 and L2 error estimates. The superconvergence of numerical derivatives at optimal stress points is discussed. Finally, the numerical experiments show the results of theoretical analysis.

关 键 词：两点边值问题 二次有限体积元法 应力佳点 误差估计 

分 类 号：O241.82[理学—计算数学]