Error analysis of first- and second-order linear, unconditionally energy-stable schemes for the Swift-Hohenberg equation

被引：3
|
作者：
Qi, Longzhao [1 ]
Hou, Yanren [1 ]
机构：
[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2022年 / 127卷
基金：
中国国家自然科学基金;
关键词：
Swift-Hohenberg equation; Invariant energy quadratization (IEQ) scheme; Energy stability; Error analysis; PHASE-FIELD MODEL; NUMERICAL APPROXIMATIONS; ADDITIVE NOISE; NEURAL FIELDS; DYNAMICS; CAHN;
D O I：
10.1016/j.camwa.2022.10.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work, we present first-and second-order energy-stable linear schemes for the Swift-Hohenberg equation based on first-order backward Euler and Crank-Nicolson schemes, respectively. We prove rigorously that the schemes satisfy the energy dissipation property. We also derive the error analysis for our schemes. Moreover, we adopt a spectral-Galerkin approximation for the spatial variables and establish error estimates for the fully discrete second-order Crank-Nicolson scheme. Numerical results are presented to validate our theoretical analysis.
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页码：192 / 212
页数：21
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