| 奇异摄动问题在Bakhvalov-Shishkin 网格上的流线扩散有限元逼近 |
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| 引用本文： | 尹云辉,祝鹏,杨宇博.奇异摄动问题在Bakhvalov-Shishkin 网格上的流线扩散有限元逼近[J].计算数学,2013,35(4):365-376. |
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| 作者姓名： | 尹云辉 祝鹏 杨宇博 |
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| 作者单位： | 1. 嘉兴学院数理与信息工程学院, 浙江嘉兴 314001;
2. 嘉兴学院南湖学院, 浙江嘉兴 314001 |
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| 基金项目： | 浙江省自然科学基金（LQ12A01014）以及嘉兴学院科研启动基金（70510017）资助。 |
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| 摘 要： | 本文采用线性插值的流线扩散有限元在Bakhvalov-Shishkin网格上求解一维对流扩散型的奇异摄动问题. 在ε ≤ N-1的前提下，可以得到，关于扰动参数ε 是一致收敛的. 在离散的SD范数下，其u-uI的误差阶提高到N-2，u-uh的误差阶达到N-2（lnN）0.5. 最后，通过数值算例，验证了理论分析.
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| 关 键 词： | 奇异摄动问题 流线扩散有限元 Bakhvalov-Shishkin 网格 |
| 收稿时间： | 2012-12-24; |
A STREAMLINE-DIFFUSION FINITE ELEMENT APPROXIMATION ON BAKHVALOV-SHISHKIN MESH FOR SINGULARLY PERTURBED PROBLEM |
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| Yin Yunhui,Zhu Peng,Yang Yubo.A STREAMLINE-DIFFUSION FINITE ELEMENT APPROXIMATION ON BAKHVALOV-SHISHKIN MESH FOR SINGULARLY PERTURBED PROBLEM[J].Mathematica Numerica Sinica,2013,35(4):365-376. |
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| Authors: | Yin Yunhui Zhu Peng Yang Yubo |
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| Institution: | 1. College of Mathematics Physics and Information Engineering, Jiaxing University, Jiaxing 314001, Zhejiang, China;
2. Nanhu College, Jiaxing University, Jiaxing 314001, Zhejiang, China |
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| Abstract: | In this paper, a linear 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. A rate O(N-2（lnN）0.5) in a discrete SD norm is established under certain regularity assumptions. Finally, through numerical experiments, we verified the theoretical results. |
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| Keywords: | singularly perturbed problem Streamline-Diffusion finite element method Bakhvalov-Shishkin mesh |
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