Immersed Interface Method for elliptic equations based on a piecewise second order polynomial
Immersed Interface Method for elliptic equations based on a piecewise second order polynomial
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基于分段二阶多项式的椭圆方程的浸入界面法
DOI：
10.1016/j.camwa.2011.11.060
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发表时间：
2012-03
期刊：
影响因子：
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通讯作者：
Li, Yongfei
中科院分区：
文献类型：
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作者：
Zhao, Jianping;Hou, Yanren;Li, Yongfei
本文研究了区域Ω∈Rd，d= 1，2中椭圆型方程的有限差分方法.在区域Ω内，我们假设有一个余维为1的不规则曲面Γ（以下称为界面），已知函数u或它的某些导数在该曲面上是不连续的。用均匀网格和分段二阶多项式逼近u，得到了求解这类问题的二阶方法。最后给出了几个实例来说明该方案的正确性和有效性。
In this paper, we develop finite difference methods for elliptic equations in a domain Ω∈Rd, d=1,2. Within the region Ω, we suppose there is an irregular surface Γ of codimension 1 (hereafter called an interface) across which the function u or some of its derivatives are known to be discontinuous. We use uniform grid and a piecewise second order polynomial to approximate u, then we get a second order method for these problems. At last, we give several examples to show the correctness and efficiency of the scheme.