Approximation of Axisymmetric Darcy Flow Using Mixed Finite Element Methods
Approximation of Axisymmetric Darcy Flow Using Mixed Finite Element Methods
复制标题
使用混合有限元方法逼近轴对称达西流
DOI：
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发表时间：
2013
影响因子：
2.9
通讯作者：
V. Ervin
中科院分区：
文献类型：
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作者：
V. Ervin
在这篇文章中，我们研究的数值逼近达西方程在轴对称区域，受轴对称数据，使用混合有限元方法。在柱坐标系中重写该问题将三维问题简化为二维问题。这种减少到两个维度需要在适当加权的希尔伯特空间中研究数值分析。在这种情况下，Raviart-托马斯（RT）和Brezzi-道格拉斯-马里尼（BDM）逼近对被证明是LBB稳定的，并推导出相应的先验误差估计。提出的数值实验证实了预测的RT和BDM近似的收敛速度。
In this article we investigate the numerical approximation of the Darcy equations in an axisymmetric domain, subject to axisymmetric data, using mixed finite element methods. Rewriting the problem in cylindrical coordinates reduces the three-dimensional problem to a problem in two dimensions. This reduction to two dimensions requires the numerical analysis to be studied in suitably weighted Hilbert spaces. In this setting the Raviart--Thomas (RT) and Brezzi--Douglas--Marini (BDM) approximation pairs are shown to be LBB stable and corresponding a priori error estimates are derived. Presented numerical experiments confirm the predicted rates of convergence for the RT and BDM approximations.