Convergence Analysis of the Shortley-Weller Method on Refinement Grids for Elliptic Equations with Singularities
Convergence Analysis of the Shortley-Weller Method on Refinement Grids for Elliptic Equations with Singularities
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奇点椭圆方程细化网格Shortley-Weller方法的收敛性分析
DOI：
10.1080/01630563.2016.1147463
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发表时间：
2016
影响因子：
1.2
通讯作者：
Ruyun Wang and Qing Fang
中科院分区：
文献类型：
--
作者：
Xiao-Yu Zhang;Ruyun Wang and Qing Fang
本文考虑Shortley-Weller方法在加细网格上应用于椭圆型偏微分方程的收敛性问题。对于有界区域Ω上的Dirichlet边值问题，当其解在Ω的部分或全部边界附近具有奇异导数时，利用多项式和指数拉伸函数进行加细.当Ω为单位平方时，证明了方法的收敛性，并通过改变拉伸函数中的参数来加速收敛。数值例子说明了如何拉伸功能的影响取决于参数的选择。
In this article, we consider the convergence problem of the Shortley-Weller method on refinement grids applied to elliptic partial differential equations. The refinement uses polynomial and exponential stretching functions for Dirichlet boundary value problems in a bounded domain Ω whose solutions have singular derivatives near a part or the whole of the boundary of Ω. In the case where Ω is the unit square, it is shown that the methods are convergent and the convergence can be accelerated by varying parameters in the stretching functions. Numerical examples are given to illustrate how the effect on the stretching functions depends upon the choice of parameters.