Abstract
In this article, we consider a temporally second-order unconditionally energy stable computational method for the Allen–Cahn (AC) equation with a high-order polynomial free energy potential. By modifying the nonlinear parts in the governing equation, we have a linear convex splitting scheme of the energy for the high-order AC equation. In addition, by combining the linear convex splitting with a strong-stability-preserving implicit–explicit Runge–Kutta (RK) method, the proposed method is linear, temporally second-order accurate, and unconditionally energy stable. Computational tests are performed to demonstrate that the proposed method is accurate, efficient, and energy stable.
Original language | English |
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Article number | 416 |
Journal | Advances in Difference Equations |
Volume | 2021 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2021 Dec |
Bibliographical note
Funding Information:The first author (J. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1A2C1003053). The corresponding author (H.G. Lee) was supported by the Research Grant of Kwangwoon University in 2021 and by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1C1C1011112).
Publisher Copyright:
© 2021, The Author(s).
Keywords
- Allen–Cahn equation
- High-order polynomial free energy
- Implicit–explicit RK scheme
- Linear convex splitting
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Applied Mathematics