Optimal Error Estimates Of The Local Discontinuous Galerkin Method And Exponential Time Differencing Schemes For The MBE Equation

The main content of this paper is optimal error estimates of the local dis-continuous Galerkin(LDG)method and exponential time differencing(ETD)schemes for the molecular beam epitaxy(MBE)equation.For spatial discretization,we present the semi-discrete LDG scheme for the MBE equation.By choosing appropriate numerical fluxes and with the properties of projection operators,we prove the corresponding error estimate.The nonlin-ear term in the MBE equation makes error estimate more difficult.By special treatment for nonlinear term,we get the optimal convergence rate of k+1 in the L~2 norm fork-th order polynomial approximation.For temporal discretization,to relax the severe time step restriction of explicit time marching methods,we employ a class of ETD schemes for time approximation.Finally,numerical exper-iments of the accuracy and long time simulation are given to show the efficiency and capability of the proposed numerical schemes.