An equation decomposition method for the numerical solution of a fourth‐order elliptic singular perturbation problem
An equation decomposition method for the numerical solution of a fourth‐order elliptic singular perturbation problem
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DOI：
10.1002/num.20666
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发表时间：
2012-05
影响因子：
3.9
通讯作者：
Houde Han;Zhongyi Huang
中科院分区：
文献类型：
--
作者：
Houde Han;Zhongyi Huang
在本文中，我们提出了一种基于方程分解技术的定制有限点方法（TFPM），用于二维四阶奇异摄动问题的数值求解。我们的有限点方法是根据局部指数基函数定制的。此外，我们的 TFPM 自动满足离散极大值原理。我们的数值例子表明，我们的方法在能量范数中的二阶收敛率为 $\varepsilon\to0$。 © 2011 Wiley periodicals, Inc. 数值方法偏微分方程，2011
In this article, we propose a tailored finite point method (TFPM) for the numerical solution of a type of fourth‐order singular perturbation problem in two dimensions based on the equation decomposition technique. Our finite point method has been tailored based on the local exponential basis functions. Furthermore, our TFPM satisfies the discrete maximum principle automatically. Our numerical examples show that our method has second order convergence rate in energy norm as $\varepsilon\to0$. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011