Improved Scalar Auxiliary Variable Schemes for Original Energy Stability of Gradient Flows

被引：1
作者：
Chen, Rui [1 ,2 ]
Wang, Tingfeng [3 ]
Zhao, Xiaofei [4 ,5 ]
机构：
[1] Beijing Univ Posts & Telecommun, Sch Sci, Beijing 100876, Peoples R China
[2] Beijing Univ Posts & Telecommun, Key Lab Math & Informat Networks Minist Educ, Beijing 100876, Peoples R China
[3] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China
[4] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China
[5] Wuhan Univ, Computat Sci Hubei Key Lab, Wuhan 430072, Peoples R China
来源：
JOURNAL OF SCIENTIFIC COMPUTING | 2025年 / 103卷 / 01期
关键词：
Gradient flows; Improved scalar auxiliary variable scheme; Original energy stability; Allen-Cahn and Cahn-Hilliard equations; Convergence; PHASE-FIELD MODELS; STABLE NUMERICAL SCHEMES; LINEAR SCHEMES; ALLEN-CAHN; EFFICIENT; 2ND-ORDER; ACCURATE; APPROXIMATIONS; ALGORITHMS; SEPARATION;
D O I：
10.1007/s10915-025-02796-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Scalar auxiliary variable (SAV) methods are a class of linear schemes for solving gradient flows that are known for the stability of a 'modified' energy. In this paper, we propose an improved SAV (iSAV) scheme that not only retains the complete linearity but also ensures rigorously the stability of the original energy. The convergence and optimal error bound are rigorously established for the iSAV scheme and discussions are made for its high-order extension. Extensive numerical experiments are done to validate the convergence, robustness and energy stability of iSAV, and some comparisons are made.
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