| 非定常Navier-Stokes方程的质量集中各向异性非协调有限元逼近 |
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| 引用本文： | 石东洋,王慧敏.非定常Navier-Stokes方程的质量集中各向异性非协调有限元逼近[J].数学物理学报(A辑),2010,30(4):1018-1029. |
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| 作者姓名： | 石东洋 王慧敏 |
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| 作者单位： | 石东洋(郑州大学数学系,郑州,450052);王慧敏(郑州大学数学系,郑州,450052;河南工程学院数理科学系,郑州,450007) |
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| 基金项目： | 国家自然科学基金，河南省教育厅自然科学勘察计划项目 |
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| 摘 要： | 该文将一个低阶Crouzeix-Raviart型非协调三角形元应用到非定常Navier-Stokes方程,给出了其质量集中有限元逼近格式.在不需要传统Ritz-Volterra投影下,通过引入两个辅助有限元空间对边界进行估计的技巧,在各向异性网格下导出了速度的L~2模和能量模及压力的L~2模的误差估计.
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| 关 键 词： | Navier-Stokes方程 质量集中 各向异性 非协调元 误差估计 |
| 收稿时间： | 2007-12-08 |
| 修稿时间： | 2009-01-15 |
The Lumped Mass Nonconforming Finite Element Approximation for the Nonstationary Navier-Stokes Equations on Anisotropic Meshes |
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| SHI Dong-Yang,WANG Hui-Min.The Lumped Mass Nonconforming Finite Element Approximation for the Nonstationary Navier-Stokes Equations on Anisotropic Meshes[J].Acta Mathematica Scientia,2010,30(4):1018-1029. |
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| Authors: | SHI Dong-Yang WANG Hui-Min |
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| Institution: | 1.Deparment of Mathematics, |Zhengzhou University, Zhengzhou 450052;
2.Department of Mathematics and Physics, Henan Institute of Engineering, Zhengzhou |450007 |
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| Abstract: | In this paper, a low order Crouzeix-Raviart type nonconforming triangular element is applied to the nonstationary Navier-Stokes equations. The approximation scheme of the lumped mass finite element methods for the problem is proposed. Without using Ritz-Volterra projection, the error estimates are derived both in the L2-norm and the energy norm for velocity and the L2-norm for pressure on anisotropic meshes through the technique of introducing two auxiliary finite element spaces to the boundary estimate. |
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| Keywords: | Navier-Stokes equationszz Lumped masszz Anisotropic mesheszz Nonconforming finite elementzz Error estimatezz |
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