This paper is concerned with numerical methods for solving the multidimensional Allen-
Cahn equations with spatial fractional Riesz derivatives. A fully discrete numerical scheme is …

This paper presents two numerical schemes for solving the Allen–Cahn equation
representing a model for antiphase domain coarsening in a binary mixture. Based on the …

In this paper, we present a local discontinuous Galerkin (LDG) method for the Allen-Cahn
equation. We prove the energy stability, analyze the optimal convergence rate of k+ 1 in L² …

In this paper, we mainly consider the numerical approximation for the Allen-Cahn (AC)
equation with logarithmic Flory–Huggins potential. It is well-known that the logarithmic Flory …

In this paper, we develop a polygonal mesh adaptation algorithm for a fully implicit scheme
based on discontinuous Galerkin (DG) finite element methods in space and backward Euler …

We propose a second order, fully semi-Lagrangian method for the numerical solution of
systems of advection-diffusion-reaction equations, which is based on a semi-Lagrangian …

In this article, we present a reduced order method for modeling and computing Allen–Cahn
equations. A global basis method is used in the discretized system of the Allen–Cahn …

This paper considers the stability and convergence of Euler implicit/explicit scheme for the
incompressible magnetohydrodynamic (MHD) equations by the scalar auxiliary variable …

In this paper, we propose a numerical method to solve the space fractional Allen-Cahn
equation. First, to remove the constraint of time step, an efficient scheme is constructed by …

In this paper, a linearized finite difference scheme is proposed for solving the multi‐
dimensional Allen–Cahn equation. In the scheme, a modified leap‐frog scheme is used for …