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.
作者
石东洋
周钱
SHI Dongyang;ZHOU Qian(School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,China)
出处
《信阳师范学院学报（自然科学版）》
CAS
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)。
