CONVERGENCE TO EQUILIBRIUM OF A DC ALGORITHM FOR AN EPITAXIAL GROWTH MODEL

Abstract : A linear numerical scheme for an epitaxial growth model is analyzed in this work. The considered scheme is already established in the literature using a convexity splitting argument. We show that it can be naturally derived from an optimization viewpoint using a DC (difference of convex functions) programming framework. Moreover, we prove the convergence of the scheme towards equilibrium by means of the Lojasiewicz-Simon inequality. The fully discrete version, based on a Fourier collocation method, is also analyzed. Finally, numerical simulations are carried out to accommodate our analyzis.