非线性BBM方程BDF2混合有限元方法的超逼近分析
Analysis on Superclose Results for Nonlinear BBM Equation with BDF2 Mixed Finite Element Method
王俊俊 1江梦萍 1关振1
作者信息
- 1. 平顶山学院 数学与统计学院,河南 平顶山 467000
- 折叠
摘要
针对非线性Benjamin-Bona-Mahony(BBM)方程,在时间上构造了 2 阶的Backward differential formula(BDF2)时间离散格式,在空间上采用双线性单元和零阶RT单元的混合有限元方法,研究了其超收敛性质.首先,利用变换技巧给出关于逼近方程的稳定性.其次,利用逼近解的有界性得到关于其原始变量u的一个超逼近结果,进而得到其中间变量( →q)的超逼近结果.最后利用一个算例验证理论结果的正确性.
Abstract
A second-order Backward Differential Formula(BDF2)time discretization scheme is constructed for the nonlinear Benjamin-Bona-Mahony(BBM)equation,and a mixed finite element method incorporating bi-linear and zero-order Raviart-Thomas(RT)elements is employed to investigate its superconvergence properties.Firstly,the stability of the approximate equation is established using certain transformation techniques.Second-ly,by utilizing the boundedness of the approximate solution,superclose results are derived.Finally,an example is presented to verify the validity of the theoretical findings.
关键词
非线性BBM方程/BDF2混合有限元方法/稳定性,超逼近分析Key words
nonlinear BBM equation/BDF2 mixed finite element method/stability/superclose analysis引用本文复制引用
出版年
2024
NETL
NSTL
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