Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation (Advances in Applied Mathematics and Mechanics, 2022)
We propose a class of up to fourth-order maximum-principle-preservingand mass-conserving schemes for the conservative Allen-Cahn equation equipped witha non-local Lagrange multiplier. Based on the second-order finite-difference semi-discretization in the spatial direction, the integrating factor Runge-Kutta schemes areapplied in the temporal direction. Theoretical analysis indicates that the proposedschemes conserve mass and preserve the maximum principle under reasonable timestep-size restriction, which is independent of the space step size. Finally, the theoreticalanalysis is verified by several numerical examples.