New Finite Element Methods in Computational Fluid Dynamics by H(div) Elements
New Finite Element Methods in Computational Fluid Dynamics by H(div) Elements
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DOI：
10.1137/060649227
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发表时间：
2007-05
期刊：
影响因子：
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通讯作者：
Junping Wang;X. Ye
中科院分区：
文献类型：
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作者：
Junping Wang;X. Ye
在本文中，作者提出了两个公式的斯托克斯问题，利用现有的$H（{\rmdiv}）$元素的Raviart-Thomas型最初开发的二阶椭圆问题。此外，还构造了两个新的H（{\rmdiv}）$元素，并对新公式进行了分析.最优阶误差估计建立相应的有限元解在各种Sobolev范数。当数值格式中采用现有的Raviart-Thomas型单元时，有限元解完全满足连续性方程。
In this paper, the authors present two formulations for the Stokes problem which make use of the existing $H({\rm div})$ elements of the Raviart-Thomas type originally developed for the second-order elliptic problems. In addition, two new $H({\rm div})$ elements are constructed and analyzed particularly for the new formulations. Optimal-order error estimates are established for the corresponding finite element solutions in various Sobolev norms. The finite element solutions feature a full satisfaction of the continuity equation when existing Raviart-Thomas-type elements are employed in the numerical scheme.