The stabilized exponential-SAV approach for the Allen–Cahn equation with a general mobility

Abstract

In this paper, we construct a second-order accurate, energy stable and maximum bound principle-preserving scheme for the Allen–Cahn equation with a general mobility based on the stabilized exponential scalar auxiliary variable (SESAV) approach. Some extra stabilizing terms are added to the discretized scheme for the purpose of improving numerical stability. We first proved the maximum bound principle (MBP) under reasonable constraints on time step size and the stabilization parameter. Then, we found that the proposed scheme is unconditionally energy-stable. Finally, a numerical example is carried out to verify the theoretical results.