CONVERGENCE ANALYSIS OF THE FINITE DIFFERENCE ADI SCHEME FOR THE HEAT EQUATION ON A CONVEX SET

被引：0
|
作者：
Bialecki, Bernard [1 ]
Dryja, Maksymilian [2 ]
Fernandes, Ryan [3 ]
机构：
[1] Colorado Sch Mines, Dept Appl Math & Stat, Golden, CO 80401 USA
[2] Warsaw Univ, Inst Appl Math & Mech, PL-02097 Warsaw, Poland
[3] Khalifa Univ Sci & Technol, Dept Math, POB 2533, Abu Dhabi, U Arab Emirates
来源：
MATHEMATICS OF COMPUTATION | 2021年 / 90卷 / 332期
关键词：
Heat equation; finite difference; ADI; convergence analysis; EMBEDDED BOUNDARY METHOD;
D O I：
10.1090/mcom/3653
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is well known that for the heat equation on a rectangle, the finite difference alternating direction implicit (ADI) method converges with order two. For the first time in the literature, we bound errors of the finite difference ADI method for the heat equation on a convex set for which it is possible to construct a partition consistent with the boundary. Numerical results indicate that the ADI method may also work for some nonconvex sets for which it is possible to construct a partition consistent with the boundary.
引用
收藏
页码：2757 / 2784
页数：28
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