Adaptive numerical method for singularly perturbed equation with periodical boundary value problem

被引：0
|
作者：
Cai X. [1 ,2 ]
Wu J.-H. [2 ]
Xu M.-S. [2 ]
Li W.-C. [2 ]
机构：
[1] College of Civil Engineering and Architecture, Zhejiang University
[2] Zhejiang University of Science and Technology
来源：
Zhejiang Daxue Xuebao (Gongxue Ban)/Journal of Zhejiang University (Engineering Science) | 2010年 / 44卷 / 11期
关键词：
Elliptic partial differential equation; Parabolic partial differential equation; Shishkin mesh; Uniform convergence;
D O I：
10.3785/j.issn.1008-973X.2010.11.031
中图分类号：
学科分类号：
摘要：
Aimed at singularly perturbed elliptic partial differential equation with periodical boundary value problem, an effective numerical method was constructed. Adaptive convergence was proved. Effective computational result was obtained with few number grid when the parameter was small. Firstly, the property of boundary layer was discussed. The solution was decomposed into the smooth component and the singular component. The derivatives of the smooth component and the singular component were estimated. Secondly, finite difference method was proposed on the Shishkin mesh. The discrete maximum principle and the uniform stability result were studied. Thirdly, uniform convergence is proved by constructing the barrier function. Finally, numerical experiment was proposed to support the theoretical result. Numerical results show that the presented method fitted the property of boundary layer well. The solution for this kind of multi-scale problem was provided in theory. The presented numerical method can be applied to calculate other singularly perturbed problems.
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页码：2214 / 2219
页数：5
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