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This article is cited in 1 scientific paper (total in 1 paper)
General numerical methods
Stability analysis of several time discrete schemes for Allen–Cahn and Cahn–Hilliard equations
Qiaoling Hea, Junping Yana, Abudurexiti Abuduwailib a College of Science, Shihezi University, 832000 Xinjiang, China
b College of Mathematics and System Science, Xinjiang University, 830046 Xinjiang, China
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 $\varphi$ is defined, where $\varphi=-1$ in Allen–Cahn equation and $\varphi=\Delta$ 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.
Key words:
Allen–Cahn equation, Cahn–Hilliard equation, mixed finite element methods, error estimates, stability analysis, positive definite operator.
Received: 23.05.2023 Revised: 23.05.2023 Accepted: 26.06.2023
Citation:
Qiaoling He, Junping Yan, Abudurexiti Abuduwaili, “Stability analysis of several time discrete schemes for Allen–Cahn and Cahn–Hilliard equations”, Zh. Vychisl. Mat. Mat. Fiz., 63:10 (2023), 1614; Comput. Math. Math. Phys., 63:10 (2023), 1773–1786
Linking options:
https://www.mathnet.ru/eng/zvmmf11628 https://www.mathnet.ru/eng/zvmmf/v63/i10/p1614
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