解一维抛物方程的基于应力佳点的二次有限体积元法  

Quadratic Finite Volume Element Methods Based on Optimal Stress Points for Solving One-Dimensional Parabolic Problems

作　　者：孙佳慧[1] 秦丹丹[1] 于长华[2] 

机构地区：[1]空军航空大学基础部,长春130022 [2]吉林大学数学研究所,长春130012

出　　处：《吉林大学学报（理学版）》2011年第4期643-651,共9页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10971082)

摘　　要：构造了求解一维抛物问题的一种新的Lagrange型二次全离散有限体积元法,取应力佳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,检验函数空间取分片常数函数空间.证明了新方法具有最优阶的H1模和L2模误差估计,并讨论了H1模的整体超收敛估计及在应力佳点导数的逐点超收敛估计.数值实验验证了理论分析结果.A new Lagrangian quadratic finite volume element method based on optimal stress points was presented for solving one-dimensional parabolic problems with trial and test spaces as the Lagrangian quadratic finite element space and the piecewise constant function space respectively.It is proved that the method has optimal order H1 and L2 error estimates.In addition,we discussed the global superconvergence in H1 norm and the locally pointwise superconvergence of numerical derivatives at optimal stress points.The numerical experiment confirms the results of theoretical analysis.

关 键 词：二次有限体积元法 抛物方程 应力佳点 误差估计 

分 类 号：O241.82[理学—计算数学]