Unconditional energy dissipation law and optimal error estimate of fast L1 schemes for a time-fractional Cahn–Hilliard problem

Abstract

In this paper, we will investigate a fully discrete semi-implicit stabilized scheme for the time-fractional Cahn–Hilliard equation, which adopts the nonuniform fast L1 scheme in time, the mixed finite element method in space, and the stabilization technique for the derivative of the double-well potential. By using the temporal–spatial splitting technique, the boundedness of L∞-norm of the computed solution Uhn is obtained. Combining this boundedness, the unconditional optimal error estimate is given without certain temporal restrictions dependent on the spatial mesh size. Moreover, with the help of the boundedness of ‖Uhn‖∞ and the positive definiteness of L1 kernels, it is shown that the proposed scheme preserves the modified discrete energy dissipation property. Finally, numerical experiments are provided to further verify our theoretical convergent result.