两点边值问题的Hermite五次元有限体积法  

Finite Volume Element Methods of Fifth-order Hermite Type for Two-point Boundary Value Problems

作　　者：田万福[1] 吕俊良[1] 王彦鹤[2] 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2期165-173,共9页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:J0630104)

摘　　要：构造求解两点边值问题的一种Hermite型五次元高精度有限体积法,其中试探函数空间取Hermite型五次有限元空间,与Hermite型三次元相同,未引入更高阶导数作为插值条件,检验函数空间取分段线性函数空间,这样构造的格式求解精度更高.并分别给出了解的H1模和L2模的最优收敛阶估计,L2模收敛阶比H1模收敛阶高一阶.数值实验结果验证了方法的有效性和正确性.We constructed a finite volume scheme of fifth-order Hermite type with high accuracy for two-point boundary value problems, choosing trial and test spaces as the fifth-order finite element space of Hermite type and the piecewise linear function space respectively. We didn＇t use higher derivatives as interpolation conditions, which is the same as the third-order finite element of Hermite type, but the scheme obtained had higher accuracy. The optimal convergence rates in H^1 and L^2 norms are proved, and the convergence order in L^2 norm is one order higher than that in H^1 norm. The numerical examples confirm the theoretical results.

关 键 词：有限体积元法 Hermite五次元 对偶剖分 两点边值问题 

分 类 号：O241.82[理学—计算数学]