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

作　　者：王俊俊 江梦萍 关振 WANG Junjun;JIANG Mengping;GUAN Zhen(School of Mathematics and Statistics,Pingdingshan University,Pingdingshan 467000,China)

机构地区：[1]平顶山学院数学与统计学院,河南平顶山467000

出　　处：《许昌学院学报》2024年第5期1-7,共7页Journal of Xuchang University

基　　金：河南省自然科学基金青年项目(222300420256,242300420655)。

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.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 bilinear 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.Secondly,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 

分 类 号：O242.21[理学—计算数学]