Year: 2019
Author: Hamza Khalfi, Morgan Pierre, Nour Eddine Alaa, Mohammed Guedda
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 3 : pp. 398–411
Abstract
A linear numerical scheme for an epitaxial growth model is analyzed in this work. The considered scheme is already established in the literature using a convexity splitting argument. We show that it can be naturally derived from an optimization viewpoint using a DC (difference of convex functions) programming framework. Moreover, we prove the convergence of the scheme towards equilibrium by means of the Lojasiewicz-Simon inequality. The fully discrete version, based on a Fourier collocation method, is also analyzed. Finally, numerical simulations are carried out to accommodate our analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2019-IJNAM-12875
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 3 : pp. 398–411
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Thin film epitaxy DC programming coarsening dynamics Lojasiewicz-Simon inequality epitaxial growth model without slope selection Fourier spectral method convergence to equilibrium pattern formation.