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) …

The motion of two contiguous incompressible and viscous fluids is described within the
diffuse interface theory by the so-called Model H. The system consists of the Navier--Stokes …

We present a novel dual-mesh based adaptive phase field method for solving fracture
problems. As the name suggests, the proposed scheme is solved using two meshes with …

We consider a well-known diffuse interface model for the study of the evolution of an
incompressible binary fluid flow in a two or three-dimensional bounded domain. This model …

In this paper, we propose a discontinuous finite volume element method to solve a phase
field model for two immiscible incompressible fluids. In this finite volume element scheme …

A fully decoupled, linearized, and unconditionally stable finite element method is developed
to solve the Cahn–Hilliard–Navier–Stokes–Darcy model in the coupled free fluid region and …

Our aim in this article is to prove the existence of solutions for a Cahn–Hilliard–Navier–
Stokes system based on the Oono model and with singular potentials (and, in particular, the …

In this paper, we propose a phase field model for the dynamics of three-component
immiscible flows on solid surface. The model is an extension of the two-component phase …

A fully decoupled, linearized, and unconditionally stable finite element method is developed
to solve the Cahn–Hilliard–Navier–Stokes–Darcy model in the coupled free fluid region and …