Optimal Error Estimates of the Semi-Discrete Local Discontinuous Galerkin Method and Exponential Time Differencing Schemes for the Thin Film Epitaxy Problem without Slope Selection

In this paper,we prove the optimal error estimates in L2 norm of the semidiscrete local discontinuous Galerkin(LDG)method for the thin film epitaxy problem without slope selection.To relax the severe time step restriction of explicit time marching methods,we employ a class of exponential time differencing(ETD)schemes for time integration,which is based on a linear convex splitting principle.Numerical experiments of the accuracy and long time simulations are given to show the efficiency and capability of the proposed numerical schemes.