TY - JOUR
T1 - Stabilized Crank-Nicolson/Adams-Bashforth Schemes for Phase Field Models
JO - East Asian Journal on Applied Mathematics
VL - 1
SP - 59
EP - 80
PY - 2018
DA - 2018/02
SN - 3
DO - http://doi.org/10.4208/eajam.200113.220213a
UR - https://global-sci.org/intro/article_detail/eajam/10847.html
KW - Allen-Cahn equation, Cahn-Hilliard equation, Crank-Nicolson scheme, Adams-Bashforth scheme, implicit-explicit method, error estimates.
AB - <p style="text-align: justify;">In this paper, stabilized Crank-Nicolson/Adams-Bashforth schemes are presented
for the Allen-Cahn and Cahn-Hilliard equations. It is shown that the proposed
time discretization schemes are either unconditionally energy stable, or conditionally
energy stable under some reasonable stability conditions. Optimal error estimates for
the semi-discrete schemes and fully-discrete schemes will be derived. Numerical experiments
are carried out to demonstrate the theoretical results.</p>