Error Analysis of a Mixed Finite Element Method for the Molecular Beam Epitaxy Model

Zhonghua Qiao, Tao Tang, Hehu Xie

Research output: Contribution to journalJournal articlepeer-review

20 Citations (Scopus)
22 Downloads (Pure)


This paper investigates the error analysis of a mixed finite element method with Crank--Nicolson time-stepping for simulating the molecular beam epitaxy (MBE) model. The fourth-order differential equation of the MBE model is replaced by a system of equations consisting of one nonlinear parabolic equation and an elliptic equation. Then a mixed finite element method requiring only continuous elements is proposed to approximate the resulting system. It is proved that the semidiscrete and fully discrete versions of the numerical schemes satisfy the nonlinearity energy stability property, which is important in the numerical implementation. Moreover, detailed analysis is provided to obtain the convergence rate. Numerical experiments are carried out to validate the theoretical results.

Original languageEnglish
Pages (from-to)184-205
Number of pages22
JournalSIAM Journal on Numerical Analysis
Issue number1
Publication statusPublished - 8 Jan 2015

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Crank-Nicolson
  • Error analysis
  • Mixed finite element
  • Molecular beam epitaxy
  • Unconditionally energy stable


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