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

作     者：Danni Zhang Ruihan Guo 

作者机构：School of Mathematics and StatisticsZhengzhou UniversityZhengzhouHenan 450001China 

出 版 物：《Advances in Applied Mathematics and Mechanics》 (应用数学与力学进展（英文）)

年 卷 期：2023年第15卷第3期

页      面：545-567页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：This work is supported by NSFC grants No.11601490. 

主　　题：Local discontinuous Galerkin method thin film epitaxy problem error estimates exponential time differencing long time simulation 

摘      要：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.