The scalar auxiliary variable (SAV) approach [42] is a very popular and efficient method to
simulate various phase field models. To save the computational cost, a new SAV approach …

In this paper, we propose several novel numerical techniques to deal with nonlinear terms in
gradient flows. These step-by-step solving schemes, termed 3S-SAV and 3S-IEQ schemes …

Abstract Recently, the viscous Cahn-Hilliard (VCH) equation has been proposed as a
phenomenological continuum model for phase separation in glass and polymer systems …

Comparing with the classical local gradient flow and phase field models, the nonlocal
models such as nonlocal Cahn–Hilliard equations equipped with nonlocal diffusion operator …

A combined scheme of the improved two-grid technique with the block-centered finite
difference method is constructed and analyzed to solve the nonlinear time-fractional …

In this study, we develop first-and second-order time-accurate energy stable methods for the
phase-field crystal equation and the Swift–Hohenberg equation with quadratic-cubic non …

An effective operator splitting scheme for solving the nonlocal Allen–Cahn equation with a
Lagrange multiplier is studied. Firstly, based on the operator splitting method, the original …

In this paper, we propose a second-order fast explicit operator splitting method for the phase
field crystal equation. The basic idea lied in our method is to split the original problem into …

Two-phase systems with surfactants have extensive applications in scientific and industrial
fields. In this paper, we consider a second-order time-accurate, highly efficient, and energy …

In this paper, we develop a novel second order in time, decoupled, energy stable finite
element scheme for simulation of Cahn-Hilliard-Hele-Shaw system. The idea of scalar …