奇异摄动问题在Bakhvalov-Shishkin网格上的有限元超收敛

FINITE ELEMENT SUPERCONVERGENCE ON BAKHVALOV-SHISHKIN MESH FOR SINGULARLY PERTURBED PROBLEM

在Bakhvalov-Shishkin网格上,利用线性插值的Galerkin有限元方法求解一维对流扩散型的奇异摄动问题.在ε≤N^(-1)的前提下,通过使用离散的能量范数,可以得到,关于扰动参数ε是一敛收敛的,其误差阶达到(?)(N^(-2)).最后,通过数值算例,验证了理论分析.

A linear Galerkin finite element method on Bakhvalov-Shishkin mesh for singularly perturbed convection - diffusion problem is analyzed. The method is shown to be convergent uniformly in the perturbation parameter z provided only that ε〈N-1. A rate O（N-2） in a discrete energy norm is established under certain regularity assumptions. Finally, through numerical experiments, we verified the theoretical results.