A Stabilized Second Order Exponential Time Differencing Multistep Method for Thin Film Growth Model Without Slope Selection
Abstract
In this paper, a stabilized second order in time accurate linear exponential time differencing (ETD) scheme for the no-slope-selection thin film growth model is presented. an artificial stabilizing term $ A{\tau}^2\frac{\mathrm{\partial}{\Delta}^2u}{\mathrm{\partial}t}$ is added to the physical model to achieve energy stability, with ETD-Based multi-step approximations and Fourier collocation spectral method applied in the time integral and spatial discretization of the evolution equation, respectively. Long time energy stability and detailed o ∞(0,T;o 2) error analysis are provided based on the energy method, with a careful estimate of the aliasing error. in addition, numerical experiments are presented to demonstrate the energy decay and convergence rate.
Recommended Citation
W. Chen et al., "A Stabilized Second Order Exponential Time Differencing Multistep Method for Thin Film Growth Model Without Slope Selection," ESAIM: Mathematical Modelling and Numerical Analysis, vol. 54, no. 3, pp. 727 - 750, EDP Sciences; Société de Mathématiques Appliquées et Industrielles, May 2020.
The definitive version is available at https://doi.org/10.1051/m2an/2019054
Department(s)
Mathematics and Statistics
Keywords and Phrases
Convergence Analysis; Epitaxial Thin Film Growth; Exponential Time Differencing; Long Time Energy Stability; Second Order Scheme
International Standard Serial Number (ISSN)
2804-7214; 2822-7840
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2023 The Authors, All rights reserved.
Creative Commons Licensing
This work is licensed under a Creative Commons Attribution 4.0 License.
Publication Date
01 May 2020
