Long-term dynamics of a stabilized time-space discretization scheme for 2D time-fractional Allen-Cahn equation with double well potential

This paper deals with the long-term discrete dynamics of 2D time -fractional Allen-Cahn equation (TFACE) with double well potential. A stabilized time -space discretization scheme is proposed to solve the equation. Under no constraint of the stepsizes, the proposed scheme is proved to be maximum -principle -preserving, energy -stability -preserving and variational -energydissipation -preserving in the discrete sense. Moreover, an error estimate of the numerical scheme is also derived. In the end, a series of numerical experiments are carried out to illustrate the obtained theoretical results.