Stability and convergence of second-order schemes for the nonlinear epitaxial growth model without slope selection

Zhonghua Qiao, Zhi Zhong Sun, Zhengru Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

34 Citations (Scopus)


We present one nonlinear and one linearized numerical schemes for the nonlinear epitaxial growth model without slope selection. Both schemes are proved to be uniquely solvable and convergent with the convergence rate of order two in a discrete L2-norm. By introducing an auxiliary variable in the discrete energy functional, the energy stability of both schemes is guaranteed regardless of the time step size, in the sense that a modified energy is monotonically nonincreasing in discrete time. Numerical experiments are carried out to support the theoretical claims.
Original languageEnglish
Pages (from-to)653-674
Number of pages22
JournalMathematics of Computation
Issue number292
Publication statusPublished - 1 Jan 2014


  • Convergence
  • Energy decay
  • Finite difference scheme
  • Linearized difference scheme
  • Molecular beam epitaxy
  • Stability

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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