TY - JOUR
T1 - Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation
AU - Chen , Xiaowei
AU - Qian , Xu
AU - Song , Songhe
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 159
EP - 181
PY - 2022
DA - 2022/10
SN - 15
DO - http://doi.org/10.4208/aamm.OA-2021-0325
UR - https://global-sci.org/intro/article_detail/aamm/21130.html
KW - Maximum-principle-preserving, mass-conserving scheme, the conservative Allen-Cahn equation.
AB - <p style="text-align: justify;">We propose a class of up to fourth-order maximum-principle-preserving
and mass-conserving schemes for the conservative Allen-Cahn equation equipped with
a non-local Lagrange multiplier. Based on the second-order finite-difference semi-discretization in the spatial direction, the integrating factor Runge-Kutta schemes are
applied in the temporal direction. Theoretical analysis indicates that the proposed
schemes conserve mass and preserve the maximum principle under reasonable time
step-size restriction, which is independent of the space step size. Finally, the theoretical
analysis is verified by several numerical examples.</p>