TY - JOUR
T1 - Unconditionally energy stable second-order numerical scheme for the Allen–Cahn equation with a high-order polynomial free energy
AU - Kim, Junseok
AU - Lee, Hyun Geun
N1 - Publisher Copyright:
© 2021, The Author(s).
PY - 2021/12
Y1 - 2021/12
N2 - 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.
AB - 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.
KW - Allen–Cahn equation
KW - High-order polynomial free energy
KW - Implicit–explicit RK scheme
KW - Linear convex splitting
UR - http://www.scopus.com/inward/record.url?scp=85114878926&partnerID=8YFLogxK
U2 - 10.1186/s13662-021-03571-x
DO - 10.1186/s13662-021-03571-x
M3 - Article
AN - SCOPUS:85114878926
SN - 1687-1839
VL - 2021
JO - Advances in Difference Equations
JF - Advances in Difference Equations
IS - 1
M1 - 416
ER -