Stability Analysis of Several Time Discrete Schemes for Allen–Cahn and Cahn–Hilliard Equations
- Authors: He Q.1, Yan J.1, Abuduwaili A.2
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Affiliations:
- College of Science, Shihezi University
- College of Mathematics and System Science, Xinjiang University
- Issue: Vol 63, No 10 (2023)
- Pages: 1614-1614
- Section: ОБЩИЕ ЧИСЛЕННЫЕ МЕТОДЫ
- URL: https://journals.rcsi.science/0044-4669/article/view/140285
- DOI: https://doi.org/10.31857/S0044466923100058
- EDN: https://elibrary.ru/FQIPWE
- ID: 140285
Cite item
Abstract
In this paper, the stability of several time discrete schemes for Allen–Cahn and Cahn–Hilliard equations and an error estimate for Cahn–Hilliard equation are analyzed. In order to discuss the Allen–Cahn and Cahn–Hilliard equations, a skew symmetric positive operator
is defined, where
in Allen–Cahn equation and
in Cahn–Hilliard equation. We analyze stabilities of some schemes for the Allen–Cahn and the Cahn–Hilliard equation. The error estimates of Cahn–Hilliard equation are based on fully discrete scheme, its main idea is to use the finite element method to discretize in space, and then use two approximate results of the elliptic projection operator to analyze. Finally, we numerically verify convergence rates of this scheme.
About the authors
Qiaoling He
College of Science, Shihezi University
Email: 106509285@qq.com
832000, Xinjiang, China
Junping Yan
College of Science, Shihezi University
Email: 106509285@qq.com
832000, Xinjiang, China
Abudurexiti Abuduwaili
College of Mathematics and System Science, Xinjiang University
Author for correspondence.
Email: 106509285@qq.com
830046, Xinjiang, China