奇异摄动问题在Bakhvalov—Shishkin网格上的Galerkin有限元逼近  

A Galerkin Finite Element Approximation on Bakhvalov—Shishkin Mesh for Singularly Perturbed Problem

作　　者：杨宇博[1] 

机构地区：[1]嘉兴学院南湖学院,浙江嘉兴314001

出　　处：《嘉兴学院学报》2012年第6期9-12,共4页Journal of Jiaxing University

基　　金：浙江省自然科学基金项目(LQ12A01014);嘉兴学院科研启动基金(70510017);嘉兴学院重点科研课题资助项目(70110X05BL)

摘　　要：采用线性Galekin有限元在Bakhvalov—Shishkin网格上求解一维对流扩散型的奇异摄动问题.证明了该方法在ε≤N-1的前提下,关于扰动参数ε是一致收敛的,其ε-加权能量范数下的误差阶为N-1,并通过数值算例,验证了理论分析.In this paper, we use a linear Galerkin finite element method on Bakhvalov--Shishkin mesh for a model singularly perturbed convection--diffusion problem. The method is shown to be convergent, uniformly in the perturbation parameter e, of order N^-1 in theε-- weighted energy norm, provided only thate ≤ N^-1 , where N is the number of mesh. Finally, through numerical experiments, we verify the theoretical results.

关 键 词：奇异摄动问题 线性Galerkin有限元 Bakhvalov-Shishkin网格 

分 类 号：O241.82[理学—计算数学]