TY - JOUR
T1 - 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
AU - Zhang , Danni
AU - Guo , Ruihan
JO - Advances in Applied Mathematics and Mechanics
VL - 3
SP - 545
EP - 567
PY - 2023
DA - 2023/02
SN - 15
DO - http://doi.org/10.4208/aamm.OA-2021-0204
UR - https://global-sci.org/intro/article_detail/aamm/21440.html
KW - Local discontinuous Galerkin method, thin film epitaxy problem, error estimates, exponential time differencing, long time simulation.
AB - <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>