Stability and error estimates of Strang splitting method for the nonlocal ternary conservative Allen-Cahn model

The nonlocal model has attracted a great attention in materials science for describing various types of material heterogeneities and defects. In this study, we consider a nonlocal ternary conservative Allen-Cahn model, where the standard Laplace operator is intentionally replaced with a spatial convolution term that aims at describing long-range interactions among particles. A linear energy stable scheme is developed based on the operator splitting method. The mass conservation, energy stability and global convergence of the new scheme are analyzed rigorously. Numerical stability and convergence of the present numerical scheme are analyzed theoretically. Two and three dimensional numerical experiments are performed to validate the theoretical analysis and the efficiency of the method.

Automated summary

The nonlocal model, which describes material heterogeneities and defects, has gained significant attention in materials science. This study focuses on a nonlocal ternary conservative Allen-Cahn model and proposes a linear energy stable scheme using a spatial convolution term. Rigorous analysis and numerical experiments validate the efficiency and stability of the proposed scheme.