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 …

This chapter surveys recent numerical advances in the phase field method for geometric
surface evolution and related geometric nonlinear partial differential equations (PDEs) …

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 …

In this paper, we develop a series of efficient numerical schemes to solve the phase field
model for homopolymer blends. The governing system is derived from the energetic …

The ubiquity of semilinear parabolic equations is clear from their numerous applications
ranging from physics and biology to materials and social sciences. In this paper, we …

The scalar auxiliary variable (SAV) method was introduced by Shen et al. in [36] and has
been broadly used to solve thermodynamically consistent PDE problems. By utilizing scalar …

Stability analyses and error estimates are carried out for a number of commonly used
numerical schemes for the Allen-Cahn and Cahn-Hilliard equations. It is shown that all 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 present two accurate and efficient numerical schemes for a phase field dendritic crystal
growth model, which is derived from the variation of a free‐energy functional, consisting of a …

In this paper we propose and analyze an energy stable numerical scheme for the Cahn–
Hilliard equation, with second order accuracy in time and the fourth order finite difference …