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) …

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 …

In this article we consider finite element methods for approximating the solution of partial
differential equations on surfaces. We focus on surface finite elements on triangulated …

The Cahn–Hilliard equation involves fourth-order spatial derivatives. Finite element
solutions are not common because primal variational formulations of fourth-order operators …

In this paper we present and analyze finite difference numerical schemes for the Cahn-
Hilliard equation with a logarithmic Flory Huggins energy potential. Both first and second …

Geometry growth laws for morphological change are developed and examined for the class
of dynamic problems where surface diffusion is the only transport mechanism and hence …

We introduce provably unconditionally stable mixed variational methods for phase-field
models. Our formulation is based on a mixed finite element method for space discretization …

A phase-field moving contact line model is presented for a two-phase system with soluble
surfactants. With the introduction of some scalar auxiliary variables, the original free energy …

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 …