We present a new numerical scheme for solving a conservative Allen–Cahn equation with a
space–time dependent Lagrange multiplier. Since the well-known classical Allen–Cahn …

The local and nonlocal Allen-Cahn equations (ACEs) have received increasing attention in
the study of the complicated interfacial problems. In this paper, we conduct a comparison …

It is well known that the classic Allen–Cahn equation satisfies the maximum bound principle
(MBP), that is, the absolute value of its solution is uniformly bounded for all time by certain …

In comparison with the Cahn–Hilliard equation, the classic Allen-Cahn equation satisfies the
maximum bound principle (MBP) but fails to conserve the mass along the time. In this paper …

Abstract The conservative Allen–Cahn equation with a nonlocal Lagrange multiplier satisfies
mass conservation and energy dissipation property. A challenge to numerically solving the …

This paper investigates some numerical methods for solving the non-local Allen–Cahn
equation with a space–time dependent Lagrange multiplier. Several types of methods …

In the present study, we propose a novel conservative Allen–Cahn (CAC) equation with a
curvature-dependent Lagrange multiplier. The proposed CAC equation has a superior …

We present an efficient numerical scheme for the conservative Allen–Cahn (CAC) equation
on various surfaces embedded in a narrow band domain in the three-dimensional space …

We propose two efficient, non-iterative, and second-order accurate algorithms to solving the
anisotropic Allen–Cahn equation with the nonlocal mass conservation. The first scheme is …

The nonlocal Allen--Cahn equation, a generalization of the classic Allen--Cahn equation by
replacing the Laplacian with a parameterized nonlocal diffusion operator, satisfies the …