@Article{IJNAM-16-3,
author = {Khalfi, Hamza and Pierre, Morgan and Nour, Eddine, Alaa and Mohammed, Guedda},
title = { Convergence to Equilibrium of a DC Algorithm for an Epitaxial Growth Model},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2019},
volume = {16},
number = {3},
pages = {398--411},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/2019-IJNAM-12875},
url = {https://global-sci.com/article/83070/convergence-to-equilibrium-of-a-dc-algorithm-for-an-epitaxial-growth-model}
}