We propose a new numerical technique to deal with nonlinear terms in gradient flows. By
introducing a scalar auxiliary variable (SAV), we construct efficient and robust energy stable …

We carry out convergence and error analysis of the scalar auxiliary variable (SAV) methods
for L^2 and H^-1 gradient flows with a typical form of free energy. We first derive H^2 …

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 …

Abstract The Molecular Beam Epitaxial model is derived from the variation of a free energy,
that consists of either a fourth order Ginzburg–Landau double well potential or a nonlinear …

We construct unconditionally stable, unconditionally uniquely solvable, and second-order
accurate (in time) schemes for gradient flows with energy of the form \int_Ω(F(∇ϕ(\bfx))+ϵ …

In this paper, we review the Fourier-spectral method for some phase-field models: Allen–
Cahn (AC), Cahn–Hilliard (CH), Swift–Hohenberg (SH), phase-field crystal (PFC), and …

For the time-fractional phase-field models, the corresponding energy dissipation law has not
been well studied on both the continuous and the discrete levels. In this work, we address …

Numerical methods for solving the continuum model of the dynamics of the molecular beam
epitaxy (MBE) require very large time simulation, and therefore large time steps become …

In this paper, we develop a general framework for constructing higher-order, unconditionally
energy-decreasing exponential time differencing Runge-Kutta (ETDRK) methods applicable …

We consider several seconder order in time stabilized semi-implicit Fourier spectral
schemes for 2D Cahn–Hilliard equations. We introduce new stabilization techniques and …