%0 Journal Article
%T Burgers方程的一类三次有限体积元方法<br>A Cubic Finite Volume Element Method for the Burgers Equation
%A 何斯日古楞
%A 张婷
%A 杨凯丽
%J International Journal of Fluid Dynamics
%P 1-8
%@ 2328-0549
%D 2022
%I Hans Publishing
%R 10.12677/IJFD.2022.101001
%X 本文对Burgers方程的初边值问题，用最佳应力点构建对偶网格剖分，并基于分片三次Lagrange插值试探函数空间和分片常数检验函数空间，构造了Crank-Nicolson三次有限体积元格式并证明了数值解的L<span><sup>2</sup></span>-模最优阶误差估计及其导数在最佳应力节点处的超收敛误差估计。最后，给出数值算例验证了理论分析结果以及所提格式的有效性。<br />
In this paper, for the initial boundary value problem of the Burgers equation, the optimal stress point is used to construct a dual partition, and based on the trial function space of piecewise cubic Lagrange interpolation and the test function space of piecewise constant, the Crank-Nicolson cubic finite volume element scheme is constructed. And the L<sup>2</sup> norm optimal order error estimate of the numerical solutions and the super-convergence error estimate of the derivative at the optimal stress node are proved. Finally, numerical examples are given to verify the theoretical analysis re-sults and the validity of the proposed scheme.
%K Burgers方程，三次有限体积元法，收敛性分析<br>Burgers Equation
%K Cubic Finite Volume Element Method
%K Convergence Analysis
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=52294