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

Abstract

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-energy-dissipation-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.