Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces

This work considers the rigorous derivation of continuum models of step motion starting from a mesoscopic Burton–Cabrera–Frank-type model following the Xiang’s work (Xiang in SIAM J Appl Math 63(1):241–258, 2002). We prove that as the lattice parameter goes to zero, for a finite time interval, a modified discrete model converges to the strong solution of the limiting PDE with first-order convergence rate.