非线性BBMB方程能量稳定有限元方法高精度分析  

High Accuracy Analysis of an Energy-Stable Fem for Nonlinear Benjamin Bona-Mahony-Burgers Equation

作　　者：王乐乐 WANG Lele(School of Mathematics,Zhengzhou University of Aeronautics,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

出　　处：《郑州航空工业管理学院学报》2024年第3期108-112,共5页Journal of Zhengzhou University of Aeronautics

基　　金：河南省高等学校重点科研项目(22A110025);河南省科技攻关项目(222102320266)。

摘　　要：文章主要研究非线性Benjamin-Bona-Mahony-Burgers(BBMB)方程的能量稳定全离散有限元格式的高精度分析。首先,证明了后向Euler全离散格式的能量稳定性,得到了H1模意义下有限元解的有界性。其次,利用上述有界性和Brouwer不动点定理证明了离散问题解的存在唯一性。再次,利用协调双线性元的特殊性质,得到了相应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有效性。In this paper,the high accuracy analysis of an energy-stable fully discrete finite element(FE)scheme for the Benjamin-Bona-Mahony-Burgers(BBMB)equation is studied.Firstly,the stability of energy of backward-Euler(B-E)fully discrete scheme is proved which leads to the boundedness of the FE solution in H1-norm.Secondly,the existence and uniqueness of solution for approximation problem are proved by employing the above boundedness and Brouwer fixed-point theorem.Thirdly,by use of the special property of bilinear element,the superclose and global su⁃perconvergence results are derived.Finally,a numerical test is given to verify the validity of the theoretical analysis.

关 键 词：BBMB方程 能量稳定格式 超逼近和超收敛分析 

分 类 号：O242.21[理学—计算数学]