(untitled) (Advances in Applied Mathematics and Mechanics, 2023)
In this paper, we prove the optimal error estimates in L^2 norm of the semi-discrete 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.