On a sinc-type MBE model

Abstract: We introduce a new sinc-type molecular beam epitaxy model which is derived from a cosine-type energy functional. The landscape of the new functional is remarkably similar to the classical MBE model with double well potential but has the additional advantage that all its derivatives are uniformly bounded. We consider first order IMEX and second order BDF2 discretization schemes. For both cases we quantify explicit time step constraints for the energy dissipation which is in good accord with the practical numerical simulations. Furthermore we introduce a new theoretical framework and prove unconditional uniform energy boundedness with no size restrictions on the time step. This is the first unconditional (i.e. independent of the time step size) result for semi-implicit methods applied to the phase field models without introducing any artificial stabilization terms or fictitious variables.