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Article Dans Une Revue International Journal of Numerical Analysis and Modeling Année : 2019

CONVERGENCE TO EQUILIBRIUM OF A DC ALGORITHM FOR AN EPITAXIAL GROWTH MODEL

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Résumé

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 analyzis.
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Dates et versions

hal-03621261 , version 1 (28-03-2022)

Identifiants

  • HAL Id : hal-03621261 , version 1

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Hamza Khalfi, Morgan Pierre, Nour Eddine Alaa, Mohammed Guedda. CONVERGENCE TO EQUILIBRIUM OF A DC ALGORITHM FOR AN EPITAXIAL GROWTH MODEL. International Journal of Numerical Analysis and Modeling, 2019, 16 (3), pp.398-411. ⟨hal-03621261⟩
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