High-order, unconditionally maximum-principle preserving finite element method for the Allen-Cahn equation

In this paper, based on the mass-lumping finite element space discretization, we incor-porate the integrating factor Runge-Kutta method and stabilization technique to develop a class of temporal up to the fourth-order unconditionally structure-preserving schemes for the Allen-Cahn equation and its conservative forms. The proposed methods are lin-ear, without requiring any post-processing or limiters, and unconditionally preserve the maximum principle and mass conservation law. Several numerical experiments verify the high-order temporal accuracy of the proposed schemes, as well demonstrate the ability to preserve the maximum principle, mass conservation, and energy stability over long peri-ods. Moreover, by the aid of numerical simulation, we show that the proposed schemes also have good performances in terms of structure-preserving with high order finite ele-ment method. (c) 2023 IMACS. Published by Elsevier B.V. All rights reserved.