Abstract
Two temporal second-order energy stable schemes with variable time step sizes are constructed for the time fractional Cahn–Hilliard model. Nonuniform L1+ formula is utilized for the discretization of the fractional derivative, while the nonlinear term is handled by the fully-implicit scheme and the scalar auxiliary variable method, respectively. By means of the recently proposed discrete gradient structure of the temporal discretization operator, the discrete energy dissipation laws are developed via a unified framework, which are stronger than the energy boundedness results reported in the previous literature. Moreover, the discrete energy decay nature coincides with the classical analogies as the fractional order tends to one. The optimal convergence rate is verified numerically, furthermore, the coarsening dynamics simulation demonstrates the efficiency of the variable-step schemes combined with the adaptive time strategy.
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