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 -

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.