The energy dissipation law and the maximum bound principle (MBP) are two important
physical features of the well-known Allen--Cahn equation. While some commonly used first …

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 …

In recent years, there has been growing interest in develo** numerical methods to retain
consistency between the partial differential equation system and its deduced equations (eg …

We present and evaluate several explicit, large time-step** algorithms for the Allen-Cahn
equation. Our approach incorporates a stabilization technique and uses Taylor series …

In this paper, we propose and analyze a linear second-order numerical method for solving
the Allen-Cahn equation with a general mobility. The proposed fully-discrete scheme is …

We propose and analyze a novel approach to construct structure preserving approximations
for the Poisson–Nernst–Planck equations, focusing on the positivity preserving and mass …

In this work, we present a conservative Allen–Cahn (CAC) equation and investigate its
unconditionally maximum principle-preserving linear numerical scheme. The operator …

In this study, an efficient dimension splitting method is developed for solving the coupled
system of three-component conserved Allen–Cahn model and incompressible Navier …

This paper establishes a structure-preserving numerical scheme for the Cahn–Hilliard
equation with degenerate mobility. First, by applying a finite volume method with upwind …

In this paper, we consider numerical approximation of a thermodynamically consistent
model of two-phase flow in porous media, which obeys an intrinsic energy dissipation law …