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Volume 15, Issue 3
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

Danni Zhang & Ruihan Guo

DOI: 10.4208/aamm.OA-2021-0204

Adv. Appl. Math. Mech., 15 (2023), pp. 545-567.

Published online: 2023-02

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  • 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.

  • Keywords

Local discontinuous Galerkin method, thin film epitaxy problem, error estimates, exponential time differencing, long time simulation.

  • AMS Subject Headings

65M10, 35L75

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-15-545, author = {Zhang , Danni and Guo , Ruihan}, 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 = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0204}, url = {http://global-sci.org/intro/article_detail/aamm/21440.html} }
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 -

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.

Zhang , Danni and Guo , Ruihan. (2023). 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. Advances in Applied Mathematics and Mechanics. 15 (3). 545-567. doi:10.4208/aamm.OA-2021-0204
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