@Article{AAMM-15-3,
author = {Zhang, Danni and Ruihan, Guo},
title = {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},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2023},
volume = {15},
number = {3},
pages = {545--567},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2021-0204},
url = {https://global-sci.com/article/72844/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}
}