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

Part of: Partial differential equations, boundary value problems

Published online by Cambridge University Press:  20 February 2017

Yunhui Yin ,
Peng Zhu  and
Bin Wang
Yunhui Yin*
Affiliation:
College of Mathematics Physics and Information Engineering, Jiaxing University, Jiaxing, Zhejiang 314001, China
Peng Zhu*
Affiliation:
College of Mathematics Physics and Information Engineering, Jiaxing University, Jiaxing, Zhejiang 314001, China
Bin Wang*
Affiliation:
College of Mechanical and Electrical Engineering, Jiaxing University, Jiaxing, Zhejiang 314001, China
*
*Corresponding author. Email addresses:yunhui.yin@163.com (Y. Yin), zhupeng.hnu@gmail.com (P. Zhu), wangbin.70s@aliyun.com (B. Wang).
*Corresponding author. Email addresses:yunhui.yin@163.com (Y. Yin), zhupeng.hnu@gmail.com (P. Zhu), wangbin.70s@aliyun.com (B. Wang).
*Corresponding author. Email addresses:yunhui.yin@163.com (Y. Yin), zhupeng.hnu@gmail.com (P. Zhu), wangbin.70s@aliyun.com (B. Wang).
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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 ∈ provided only that ∈ ≤ N–1. An convergent rate in a discrete streamline-diffusion norm is established under certain regularity assumptions. Finally, through numerical experiments, we verified the theoretical results.

Keywords

singularly perturbed problemStreamline-Diffusion finite element methodBakhvalov-Shishkin mesherror estimate

MSC classification

Secondary: 65N15: Error bounds 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 10 , Issue 1 , February 2017 , pp. 44 - 64
Copyright
Copyright © Global-Science Press 2017 

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