An immersed hybrid difference method for the elliptic interface equation

被引：2

作者：

Jeon, Youngmok ^{[1
]}

机构：

[1] Ajou Univ, Dept Math, Suwon 16499, South Korea

来源：

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2022年 / 39卷 / 02期

基金：

新加坡国家研究基金会;

关键词：

Elliptic interface problem; Hybrid difference method; Immersed interface; VR transformation; FINITE-ELEMENT-METHOD; BOUNDARY METHOD; POISSON PROBLEMS; ORDER; CONVERGENCE; COEFFICIENTS; ACCURACY;

D O I：

10.1007/s13160-022-00503-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose an immersed hybrid difference (IHD) method for elliptic interface problems. An essential feature of the IHD method lies in the VR(virtual to real) transformation, which makes it possible to derive accurate finite difference approximations with functions of low regularity on interface cells. The VR transformation is consisting of the interface conditions in addition to the consistency equations, which are derived from the governing equation. The method is easy to be implemented and high order methods are conveniently derived. Numerical tests on several types of interfaces with low and high order methods are presented, which demonstrates efficiency of the IHD method. Numerical analysis for the one dimensional case is provided.

引用

页码：669 / 692

页数：24

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