BBM-Burgers方程的非协调有限元方法的超收敛分析  

Superconvergence Analysis of Nonconforming Finite Element Method for BBM-Burgers Equation

作　　者：石东洋 周钱 SHI Dongyang;ZHOU Qian(School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,China)

机构地区：[1]郑州大学数学与统计学院,河南郑州450001

出　　处：《信阳师范学院学报（自然科学版）》2024年第2期182-189,共8页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11671369,12071443)。

摘　　要：研究Benjamin-Bona-Mahony-Burgers(BBM-Burgers)方程的非协调EQ_(1)^(rot)元的线性化BDF格式下的超收敛性质。通过使用数学归纳法来处理非线性项,并利用该单元已有的高精度结果及插值后处理技术,得到了在对空间剖分尺度和时间步长无网格比约束的前提下,关于离散H^(1)-模意义下具有O(h^(2)+τ^(2))阶的超逼近和超收敛结果。最后,通过给出数值算例验证了理论分析的正确性。The superconvergence behavior of the linearized BDF format with the nonconforming EQ_(1)^(rot) element for the Benjamin-Bona-Mahony-Burgers(BBM-Burgers)equation was studied.By using mathematical induction to deal with the nonlinear term,together with the high accuracy analysis of this element and interpolation post-processing technique,then the superclose and superconvergence results of order O(h^(2)+τ^(2)) were derived in the broken H^(1)-norm without any restriction between the mesh size and time step.Finally,the correctness of the theoretical analysis was verified by a numerical example.

关 键 词：BBM-Burgers方程 非协调EQ_(1)^(rot)元 线性化BDF全离散格式 超逼近 超收敛 

分 类 号：O242.21[理学—计算数学]