Energy-stable and boundedness preserving numerical schemes for the Cahn-Hilliard equation with degenerate mobility

Abstract

Two new numerical schemes to approximate the Cahn-Hilliard equation with degenerate mobility (between stable values 0 and 1) are presented, by using two different non-centered approximation of the mobility. We prove that both schemes are energy stable and preserve the maximum principle approximately, i.e. the amount of the solution being outside of the interval [0, 1] goes to zero in terms of a truncation parameter. Additionally, we present several numerical results in order to show the accuracy and the well behavior of the proposed schemes, comparing both schemes and the corresponding centered scheme.