On linear schemes for a Cahn–Hilliard diffuse interface model

Abstract

Numerical schemes to approximate the Cahn–Hilliard equation have been widely studied in recent times due to its connection with many physically motivated problems. In this work we propose two type of linear schemes based on different ways to approximate the double-well potential term. The first idea developed in the paper allows us to design a linear numerical scheme which is optimal from the numerical dissipation point of view meanwhile the second one allows us to design unconditionally energy-stable linear schemes (for a modified energy). We present first and second order in time linear schemes to approximate the CH problem, detailing their advantages over other linear schemes that have been previously introduced in the literature. Furthermore, we compare all the schemes through several computational experiments.