This book discusses classical results, as well as recent developments, related to the Cahn–
Hilliard equation. It is based on the lectures that I gave at the CBMS-NSF Conference on the …

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 …

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 …

In this paper, we review the recent development of phase-field models and their numerical
methods for multi-component fluid flows with interfacial phenomena. The models consist of a …

How to develop efficient numerical schemes while preserving energy stability at the discrete
level is challenging for the three-component Cahn–Hilliard phase-field model. In this paper …

In this paper we construct two classes, based on stabilization and convex splitting, of
decoupled, unconditionally energy stable schemes for Cahn--Hilliard phase-field models of …

In this paper, we consider the numerical solution of a binary fluid–surfactant phase field
model, in which the free energy contains a nonlinear coupling entropy, a Ginzburg–Landau …

Our aim in this article is to discuss recent issues related with the Cahn-Hilliard equation in
phase separation with the thermodynamically relevant logarithmic potentials; in particular …

We present an efficient time-step** scheme for simulations of the coupled Navier–Stokes
Cahn–Hilliard equations for the phase field approach. The scheme has several attractive …