Burgers方程的一类三次有限体积元方法
A Cubic Finite Volume Element Method for the Burgers Equation
DOI: 10.12677/IJFD.2022.101001, PDF,    科研立项经费支持
作者: 何斯日古楞：呼和浩特民族学院，数学与大数据学院，内蒙古 呼和浩特；张 婷, 杨凯丽：内蒙古大学，数学科学学院，内蒙古 呼和浩特
关键词: Burgers方程；三次有限体积元法；收敛性分析；Burgers Equation； Cubic Finite Volume Element Method； Convergence Analysis
摘要: 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L2-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。
Abstract: 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 L2 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.
文章引用：何斯日古楞, 张婷, 杨凯丽. Burgers方程的一类三次有限体积元方法[J]. 流体动力学, 2022, 10(1): 1-8. https://doi.org/10.12677/IJFD.2022.101001

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