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Volume 10, Issue 1
Analysis of a Streamline-Diffusion Finite Element Method on Bakhvalov-Shishkin Mesh for Singularly Perturbed Problem

Yunhui Yin, Peng zhu & Bin Wang

DOI: 10.4208/nmtma.2017.y13026

Numer. Math. Theor. Meth. Appl., 10 (2017), pp. 44-64.

Published online: 2017-10

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  • 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.

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@Article{NMTMA-10-44, author = {Yunhui Yin, Peng zhu and Bin Wang}, title = {Analysis of a Streamline-Diffusion Finite Element Method on Bakhvalov-Shishkin Mesh for Singularly Perturbed Problem}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2017}, volume = {10}, number = {1}, pages = {44--64}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2017.y13026}, url = {http://global-sci.org/intro/article_detail/nmtma/12335.html} }
TY - JOUR T1 - Analysis of a Streamline-Diffusion Finite Element Method on Bakhvalov-Shishkin Mesh for Singularly Perturbed Problem AU - Yunhui Yin, Peng zhu & Bin Wang JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 44 EP - 64 PY - 2017 DA - 2017/10 SN - 10 DO - http://doi.org/10.4208/nmtma.2017.y13026 UR - https://global-sci.org/intro/article_detail/nmtma/12335.html KW - AB -

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.

Yunhui Yin, Peng zhu and Bin Wang. (2017). Analysis of a Streamline-Diffusion Finite Element Method on Bakhvalov-Shishkin Mesh for Singularly Perturbed Problem. Numerical Mathematics: Theory, Methods and Applications. 10 (1). 44-64. doi:10.4208/nmtma.2017.y13026
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