Energy stability and error estimates of exponential time differencing schemes for the epitaxial growth model without slope selection

Lili Ju, Xiao Li, Zhonghua Qiao, Hui Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

42 Citations (Scopus)

Abstract

In this paper, we propose a class of exponential time differencing (ETD) schemes for solving the epitaxial growth model without slope selection. A linear convex splitting is first applied to the energy functional of the model, and then Fourier collocation and ETD-based multistep approximations are used respectively for spatial discretization and time integration of the corresponding gradient flow equation. Energy stabilities and error estimates of the first and second order ETD schemes are rigorously established in the fully discrete sense. We also numerically demonstrate the accuracy of the proposed schemes and simulate the coarsening dynamics with small diffusion coefficients. The results show the logarithm law for the energy decay and the power laws for growth of the surface roughness and the mound width, which are consistent with the existing theories in the literature.
Original languageEnglish
Pages (from-to)1859-1885
Number of pages27
JournalMathematics of Computation
Volume87
Issue number312
DOIs
Publication statusPublished - 1 Jan 2018

Keywords

  • Energy stability
  • Error estimates
  • Exponential time differencing
  • Fourier collocation
  • Linear convex splitting
  • Thin film growth

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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