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

  • 摘要: 研究Benjamin-Bona-Mahony-Burgers (BBM-Burgers)方程的非协调EQ1rot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H1-模意义下具有O(h2+τ2)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。

     

    Abstract: The superconvergence behavior of the linearized BDF format with the nonconforming EQ1rot 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(h2+τ2) were derived in the broken H1-norm without any restriction between the mesh size and time step. Finally, the correctness of the theoretical analysis was verified by a numerical example.

     

/

返回文章
返回