Unconditional superconvergence analysis of an energy conservation scheme with Galerkin FEM for nonlinear Benjamin-Bona-Mahony equation

被引:5
作者
Shi, Dongyang [1 ]
Qi, Zhenqi [1 ]
机构
[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China
来源
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2023年 / 127卷
基金
中国国家自然科学基金;
关键词
BBM equation; Galerkin FEM; Energy conservation scheme; Unconditional superconvergent error estimate; FINITE-ELEMENT-METHOD; ERROR ANALYSIS; BBM EQUATION; CONVERGENCE;
D O I
10.1016/j.cnsns.2023.107572
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, a general energy conservation Crank-Nicolson (CN) fully-discrete finite element method (FEM) scheme is developed for solving the nonlinear Benjamin-Bona-Mahony (BBM) equation, and the unconditional supercloseness and superconvergence behavior are discussed with the nonconforming EQ(1)(rot) element. Different from the time-space splitting technique, the boundedness of numerical solution in the broken H-1-norm is obtained directly based on the above energy conservation property, and the well-posedness of numerical solution is proved rigorously through the Brouwer fixed point theorem. Then, with the help of the special characters of this element and the interpolation post-processing technique, the unconditional superclose and superconvergence results are deduced strictly without any restriction between mesh size h and time step tau. Further, our analysis is extended to some other popular conforming and nonconforming finite elements. Finally, two numerical experiments are implemented to confirm the theoretical analysis. It is worth mentioning that this paper not only improve the previous results, but also can be regard as a framework for solving the BBM equation and some other PDEs with Galerkin FEMs.
引用
收藏
页数:16
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