High-order finite-difference ghost-point methods for elliptic problems in domains with curved boundaries

被引：0

作者：

Coco, Armando ^{[1
]}

Russo, Giovanni ^{[1
]}

机构：

[1] Univ Catania, Dept Math & Comp Sci, Catania, Sicily, Italy

来源：

OPEN MATHEMATICS | 2024年 / 22卷 / 01期

关键词：

unfitted boundary methods; ghost-point method; elliptic equation; high-order method; arbitrary domains; level-set method; LEVEL-SET; MULTIGRID METHODS; EQUATION;

D O I：

10.1515/math-2024-0072

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, a fourth-order finite-difference ghost-point method for the Poisson equation on regular Cartesian mesh is presented. The method can be considered the high-order extension of the second-order ghost method introduced earlier by the authors. Three different discretizations are considered, which differ in the stencil that discretizes the Laplacian and the source term. It is shown that only two of them provide a stable method. The accuracy of such stable methods is numerically verified on several test problems.

引用

页数：22

共 26 条

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