@article{021271125c4643dca21ceffde3b8ace4,
title = "Error Analysis of a Mixed Finite Element Method for the Molecular Beam Epitaxy Model",
abstract = "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.",
keywords = "Crank-Nicolson, Error analysis, Mixed finite element, Molecular beam epitaxy, Unconditionally energy stable",
author = "Zhonghua Qiao and Tao Tang and Hehu Xie",
note = "Funding information: The research of the first and third authors was partially supported by the AMSS-PolyU Joint Research Institute. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China (
[email protected]). The research of this author was partially supported by Hong Kong RGC grant PolyU 2021/12P and by Hong Kong Polytechnic University grants A-PL61 and 1-ZV9Y. Institute of Theoretical and Computational Studies and Department of Mathematics, Hong Kong Baptist University, Hong Kong, China (
[email protected]). This author{\textquoteright}s work was supported by Hong Kong Research Grants Council CERG grants and by Hong Kong Baptist University FRG grants. LSEC, ICMSEC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China (
[email protected]). The research of this author was supported in part by the National Science Foundation of China through NSFC (11371026, 91330202, 11001259, 11031006, and 2011CB309703), by the National Center for Mathematics and Interdisciplinary Science, and by the President Foundation of AMSS-CAS. Publisher copyright: {\textcopyright} 2015, Society for Industrial and Applied Mathematics",
year = "2015",
month = jan,
day = "8",
doi = "10.1137/120902410",
language = "English",
volume = "53",
pages = "184--205",
journal = "SIAM Journal on Numerical Analysis",
issn = "0036-1429",
publisher = "Society for Industrial and Applied Mathematics (SIAM)",
number = "1",
}