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

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.