Convergence of a fast explicit operator splitting method for the epitaxial growth model with slope selection

Abstract

A fast explicit operator splitting method for the epitaxial growth model with slope selection has been presented in [Cheng et al., T. Comput. Phys., 303 (2015), pp. 45-65]. The original problem is split into linear and nonlinear subproblems. For the linear part, the pseudospectral method is adopted; for the nonlinear part, a 33-point difference scheme is constructed. Here, we give a compact center-difference scheme involving fewer points for the nonlinear subproblem. In addition, we analyze the convergence rate of the algorithm. The global error order O(T-2 + h(4)) in discrete L-2-norm is proved theoretically and verified numerically. Some numerical experiments show the robustness of the algorithm for small coefficients of the fourth-order term for the one-dimensional case. In addition, coarsening dynamics are simulated in large domains and the 1/3 power laws are observed for the two-dimensional case.