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

Phase-field modeling is an effective but computationally expensive method for capturing the
mesoscale morphological and microstructure evolution in materials. Hence, fast and …

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

We develop a conservative, second-order accurate fully implicit discretization of the Navier–
Stokes (NS) and Cahn–Hilliard (CH) system that has an associated discrete energy …

This paper describes a phase field method for the optimization of multimaterial structural
topology with a generalized Cahn–Hilliard model. Similar to the well-known simple isotropic …

We propose a stable and conservative finite difference scheme to solve numerically the
Cahn-Hilliard equation which describes a phase separation phenomenon. Numerical …

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

In this work, we will analyze a class of large time-stepping methods for the Cahn–Hilliard
equation. The equation is discretized by Fourier spectral method in space and semi-implicit …

Nonlinear evolution equations are widely used to describe nonlinear phenomena in natural
and social sciences. However, they are usually quite difficult to solve in most instances. This …

We propose a new procedure for designing by rote finite difference schemes that inherit
energy conservation or dissipation property from nonlinear partial differential equations …