Numer. Math. Theor. Meth. Appl., 10 (2017), pp. 44-64.
Published online: 2017-10
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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.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2017.y13026}, url = {http://global-sci.org/intro/article_detail/nmtma/12335.html} }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.