Energy Stable BDF2-SAV Scheme on Variable Grids for the Epitaxial Thin Film Growth Models

The second-order backward differential formula (BDF2) and the scalar auxiliary variable (SAV) approach are applied to construct the linearly energy stable numerical scheme with the variable time steps for the epitaxial thin film growth models. Under the step-ratio condition 0[see formula in PDF]4.864, the modified energy dissipation law is proven at the discrete levels with regardless of time step size. Numerical experiments are presented to demonstrate the accuracy and efficiency of the proposed numerical scheme.