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

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

Year:    2017

Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 1 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2017.y13026

Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 1 : pp. 44–64

Published online:    2017-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:   

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