TY - JOUR
T1 -  Convergence to Equilibrium of a DC Algorithm for an Epitaxial Growth Model
AU - Khalfi , Hamza
AU - Pierre , Morgan
AU - Alaa , Nour Eddine
AU - Guedda , Mohammed
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 398
EP - 411
PY - 2018
DA - 2018/11
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/12875.html
KW - Thin film epitaxy, DC programming, coarsening dynamics, Lojasiewicz-Simon
inequality, epitaxial growth, model without slope selection, Fourier spectral method, convergence
to equilibrium, pattern formation.
AB - <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>