Analysis of a Streamline-Diffusion Finite Element Method on Bakhvalov-Shishkin Mesh for Singularly Perturbed Problem

Abstract

In this paper, a bilinear Streamline-Diffusion 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 $ϵ$ provided only that $ϵ ≤ N^{−1}$. An $\mathcal{O}(N^{−2}$(ln$N$)$^{1/2}$) convergent rate in a discrete streamline-diffusion norm is established under certain regularity assumptions. Finally, through numerical experiments, we verified the theoretical results.