A B-spline finite element method for solving a class of nonlinear parabolic equations modeling epitaxial thin-film growth with variable coefficient

A B-spline finite element method for solving a class of nonlinear parabolic equations modeling epitaxial thin-film growth with variable coefficient

Abstract In this paper, we propose an efficient B-spline finite element method for a class of fourth order nonlinear differential equations with variable coefficient. For the temporal discretization, we choose the Crank–Nicolson scheme. Boundedness and error estimates are rigorously derived for both...

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Bibliographic Details
Main Authors: Dandan Qin, John Jiawei Tan, Bo Liu, Wenzhu Huang
Format: Article
Language:English
Published: SpringerOpen 2020-04-01
Series:Advances in Difference Equations
Subjects:
B-spline
Finite element method
Nonlinear parabolic equation
Variable coefficient
Boundedness
Online Access:http://link.springer.com/article/10.1186/s13662-020-02629-6
Description
Summary:Abstract In this paper, we propose an efficient B-spline finite element method for a class of fourth order nonlinear differential equations with variable coefficient. For the temporal discretization, we choose the Crank–Nicolson scheme. Boundedness and error estimates are rigorously derived for both semi-discrete and fully discrete schemes. A numerical experiment confirms our theoretical analysis.
ISSN:1687-1847

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