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 …

Efficient and energy stable high order time marching schemes are very important but not
easy to construct for the study of nonlinear phase dynamics. In this paper, we propose and …

This letter introduces novel linear relaxation schemes for solving the phase field models,
particularly the Allen–Cahn (AC) type and Cahn–Hilliard (CH) type equations. The proposed …

It is known that the Allen-Chan equations satisfy the maximum principle. Is this true for
numerical schemes? To the best of our knowledge, the state-of-art stability framework is the …

In this paper, we consider finite difference method for solving Allen–Cahn equation which
contains small perturbation parameters and strong nonlinearity. We use a stabilized second …

Abstract Numerical approximations of Cahn-Hilliard phase-field model for the two-phase
incompressible flows are considered in this paper. Several efficient and energy stable time …

We carry out rigorous error analysis for some energy stable time discretization schemes
developed in Shen and Yang (SIAM J Sci Comput 32 (3): 1159–1179, 2010) for a Cahn …

In this paper, we consider the numerical approximation for a phase field model of the
coupled two-phase free flow and two-phase porous media flow. This model consists of Cahn …

Abstract The Allen–Cahn equation is one of fundamental equations of phase-field models,
while the logarithmic Flory–Huggins potential is one of the most useful energy potentials in …

Compared with the well-known classical Allen–Cahn equation, the modified Allen–Cahn
equation, which is equipped with a nonlocal Lagrange multiplier or a local-nonlocal …