一维奇异摄动问题在Shishkin网格上的流线扩散有限元逼近  

A Streamline-Diffusion Finite Element Approximation on Shishkin Mesh for 1-D Singularly Perturbed Problem

作　　者：尹云辉[1] 

机构地区：[1]嘉兴学院数理与信息工程学院,浙江嘉兴314001

出　　处：《嘉兴学院学报》2013年第3期29-34,共6页Journal of Jiaxing University

摘　　要：采用线性插值的流线扩散有限元在Shishkin网格上求解一维对流扩散型的奇异摄动问题.在ε≤N-1的前提下,可以得到关于扰动参数是一致收敛的的结论 .在离散的SD范数下,其误差阶达到N-2 ln2 N;最后,通过数值算例,验证了理论分析.In this paper, a linear Streamline- Diffusion finite element method on Shishkin mesh for singularly perturbed convection - diffusion problem is analyzed. The method is shown to be convergent uniformly in the perturbation parametereprovided only thatε≤N^（-1） A rate N^（-2）ln^2N in a discrete SD norm is established under certain regularity assumptions. Finally, through numerical experiments, we verified the theoretical results.

关 键 词：奇异摄动问题 流线扩散有限元 SHISHKIN网格 

分 类 号：O241.82[理学—计算数学]