STABILIZED FINITE ELEMENT METHODS BASED ON MULTISCALE ENRICHMENT FOR ALLEN-CAHN AND CAHN-HILLIARD EQUATIONS

被引：0
|
作者：
Wen, Juan [1 ]
He, Yaling [2 ]
He, Yinnian [3 ]
Wang, Kun [4 ]
机构：
[1] Xian Univ Technol, Sch Sci, Xian 710048, Shaanxi, Peoples R China
[2] Xi An Jiao Tong Univ, Sch Energy & Power Engn, Key Lab Thermo Fluid Sci & Engn, Minist Educ, Xian 710049, Shaanxi, Peoples R China
[3] Xi An Jiao Tong Univ, Ctr Computat Geosci 1, Sch Math & Stat, Xian 710049, Peoples R China
[4] Chongqing Univ, Coll Math & Stat, Chongqing, Peoples R China
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2022年 / 21卷 / 06期
基金：
国家重点研发计划;
关键词：
Allen-Cahn equation; Cahn-Hilliard equation; multiscale enrichment; semi-implicit scheme; error analysis; energy Stability; LINEAR SCHEMES; MODEL; APPROXIMATIONS; ENERGY; FLUIDS;
D O I：
10.3934/cpaa.2021074
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate fully discrete schemes for the Allen-Cahn and Cahn-Hilliard equations respectively, which consist of the stabilized finite element method based on multiscale enrichment for the spatial discretization and the semi-implicit scheme for the temporal discretization. With reasonable stability conditions, it is shown that the proposed schemes are energy stable. Furthermore, by defining a new projection operator, we deduce the optimal L-2 error estimates. Some numerical experiments are presented to confirm the theoretical predictions and the efficiency of the proposed schemes.
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页码：1873 / 1894
页数：22
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