二阶非线性抛物方程的B样条有限元法

Journal of Jilin University Science Edition ›› 2024, Vol. 62 ›› Issue (4): 878-885.

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B-Spline Finite Element Method of Second Order Nonlinear Parabolic Equation

QIN Dandan¹, WANG Daming¹, HUANG Wenzhu²

1. Department of Foundation, Aviation University of Air Force, Changchun 130022, China;
2. School of Biology and Engineering, Guizhou Medical University, Guiyang 550025, China

Received:2023-12-01 Online:2024-07-26 Published:2024-07-26

Abstract

Abstract: Firstly, we uesd the quadratic B-spline finite element method to solve the Fisher-Kolmogorov (FK) equation, and proved the stability and convergence of solutions for the semi-discrete scheme and the fully discrete scheme. Secondly, the time variable was discretized by using the Crank-Nicolson method and the convergence order of the approximate solution was O((Δt)²+h³). Finally, the numerical example verified theoretical analysis results and the effectiveness of the B-spline finite element method.

Key words: Fisher-Kolmogorov equation, quadratic B-spline finite element method, stability, convergence

CLC Number:

O241.82

QIN Dandan, WANG Daming, HUANG Wenzhu. B-Spline Finite Element Method of Second Order Nonlinear Parabolic Equation[J].Journal of Jilin University Science Edition, 2024, 62(4): 878-885.

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B-Spline Finite Element Method of Second Order Nonlinear Parabolic Equation

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