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
Year: 2023
Author: Danni Zhang, Ruihan Guo
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 3 : pp. 545–567
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0204
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 3 : pp. 545–567
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Local discontinuous Galerkin method thin film epitaxy problem error estimates exponential time differencing long time simulation.