非线性Benjamin-Bona-Mahony-Burgers方程的非协调有限元超收敛分析  

Superconvergent Analysis of Nonconforming Finite Element Method for the Nonlinear Benjamin-Bona-Mahony-Burgers Equation

作　　者：廖歆[1] 赵国营 LIAO Xin;ZHAO Guoying(School of Mathematics,Zhengzhou University of Aeronautics,Zhengzhou 450046,China;Unit 32738 of PLA,Zhengzhou 450046,China)

机构地区：[1]郑州航空工业管理学院数学学院,河南郑州450046 [2]32738部队,河南郑州450046

出　　处：《郑州航空工业管理学院学报》2024年第2期102-107,共6页Journal of Zhengzhou University of Aeronautics

基　　金：河南省科技攻关项目(222102210228)。

摘　　要：文章研究了二维非线性Benjamin-Bona-Mahony-Burgers(BBMB)方程的非协调有限元方法。利用非协调EQ^(rot)_(1)元相容误差比插值误差高一阶的特殊性质,给出了非线性BBMB方程在半离散以及向后Euler全离散格式下的超逼近和整体超收敛结果。最后,通过数值试验验证了理论分析的正确性和方法的有效性。In this paper,we study the nonconforming finite element method for the Benjamin-Bona-Mahony-Burgers(BBMB for short)equation.By use of the special property of the nonconforming EQ^(rot)_(1) element:the consistency error is one order higher than its interpolation error,the superclose and superconcergence results in semi-discrete and Euler full discrete schemes are obtained for this equation.Finally,a numerical example is provided to illustrate validity and efficiency of our theoretical analysis and method.

关 键 词：非线性BBMB方程 非协调EQ^(rot)_(1)元 半离散格式 向后Euler全离散格式 超逼近和超收敛 

分 类 号：O241.82[理学—计算数学]