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

Advances in Difference Equations

article

Qin, Dandan¹  Tan, Jiawei²  Liu, Bo²  Huang, Wenzhu⁴ 

[1] Fundamental Department, Aviation University of Air Force;College of Mathematics, Jilin University;School of Mathematics and Statistics, Changchun University of Technology;School of Biology and Engineering, Guizhou Medical University

关键词: B-spline;    Finite element method;    Nonlinear parabolic equation;    Variable coefficient;    Boundedness;   

DOI  :  10.1186/s13662-020-02629-6

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY