A Novel Second-Order Scheme for the Molecular Beam Epitaxy Model with Slope Selection (Communications in Computational Physics, 2018)
Molecular beam epitaxy (MBE) is an important and challenging researchtopic in material science. In this paper, we propose a new fully discrete scheme forthe well-celebrated continuum MBE model with slope selection. First of all, we use amulti-step strategy to discretize the MBE model in time. The obtained semi-discretescheme is proved to possess properties of total mass conservation, unconditionally energy stability and uniquely solvability. The rigorous error estimate is then conductedto show its second-order convergence. The semi-discrete scheme is further discretizedin space using the Fourier pseudo-spectral method. The fully discrete scheme is alsoshown to preserve mass-conservation and energy-dissipation properties. Afterward,several numerical examples are presented to validate the accuracy and efficiency ofour proposed scheme. In particular, the scaling law for the roughness growing andeffective energy decaying are captured during long-time coarsening dynamic simulations. The idea proposed in this paper could be readily utilized to design accurate andstable numerical approximations for many other energy-based phase field models.