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research-article

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

Authors:

Hehu XieAuthors Info & Claims

SIAM Journal on Numerical Analysis, Volume 53, Issue 1

Pages 184 - 205

https://doi.org/10.1137/120902410

Published: 01 January 2015 Publication History

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.

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Cited By

Qi L(2024)Numerical analysis of a second-order energy-stable finite element method for the Swift-Hohenberg equationApplied Numerical Mathematics10.1016/j.apnum.2023.11.014197:C(119-142)Online publication date: 1-Mar-2024
https://dl.acm.org/doi/10.1016/j.apnum.2023.11.014
Sun YZhou Q(2022)Error Estimate of Exponential Time Differencing Runge-Kutta Scheme for the Epitaxial Growth Model Without Slope SelectionJournal of Scientific Computing10.1007/s10915-022-01977-793:1Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1007/s10915-022-01977-7

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Published In

cover image SIAM Journal on Numerical Analysis

SIAM Journal on Numerical Analysis Volume 53, Issue 1

2015

633 pages

ISSN:0036-1429

DOI:10.1137/sjnaam.53.1

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© 2015, Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 2015

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Cited By

Qi L(2024)Numerical analysis of a second-order energy-stable finite element method for the Swift-Hohenberg equationApplied Numerical Mathematics10.1016/j.apnum.2023.11.014197:C(119-142)Online publication date: 1-Mar-2024
https://dl.acm.org/doi/10.1016/j.apnum.2023.11.014
Sun YZhou Q(2022)Error Estimate of Exponential Time Differencing Runge-Kutta Scheme for the Epitaxial Growth Model Without Slope SelectionJournal of Scientific Computing10.1007/s10915-022-01977-793:1Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1007/s10915-022-01977-7

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