Error analysis of the Crank-Nicolson SAV method for the Allen-Cahn equation on variable grids

被引：5
|
作者：
Yu, Fan [1 ]
Chen, Minghua [1 ]
机构：
[1] Lanzhou Univ, Sch Math & Stat, Gansu Key Lab Appl Math & Complex Syst, Lanzhou 730000, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2022年 / 125卷
基金：
中国国家自然科学基金;
关键词：
Allen-Cahn equation; Variable step sizes; Scalar auxiliary variable; Convergence analysis; SCHEMES;
D O I：
10.1016/j.aml.2021.107768
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The variable time-stepping technique is powerful in capturing the multi-scale behaviors (e.g., the solution changes rapidly in certain regions of time) for the Allen-Calm equation. Based on the scalar auxiliary variable (SAV) approach and the Crank-Nicolson schemes, we establish the unconditional energy stability and error estimates rigorously for the Allen-Cahn equation on variable grids. A numerical experiment is performed to verify the theoretical results. To the best of our knowledge, this is the first topic on the convergence analysis for the SAV schemes on variable grids. (C) 2021 Elsevier Ltd. All rights reserved.
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