A two-level finite element method for the Allen–Cahn equation

We consider the fully implicit treatment for the nonlinear term of the Allen–Cahn equation. To solve the nonlinear problem efficiently, the two-level scheme is employed. We obtain the discrete energy law of the fully implicit scheme and two-level scheme with finite element method. Also, the convergence of the two-level method is presented. Finally, some numerical experiments are provided to confirm the theoretical analysis.