| 解Stokes特征值问题的一种两水平稳定化有限元方法 |
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| 引用本文： | 黄鹏展,何银年,冯新龙.解Stokes特征值问题的一种两水平稳定化有限元方法[J].应用数学和力学,2012,33(5):588-597. |
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| 作者姓名： | 黄鹏展 何银年 冯新龙 |
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| 作者单位： | 新疆大学 数学与系统科学学院, 乌鲁木齐 830046; |
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| 基金项目： | 国家自然科学基金资助项目，国家863基金资助项目，新疆自然科学基金资助项目 |
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| 摘 要： | 基于局部Gauss积分,研究了解Stokes特征值问题的一种两水平稳定化有限元方法．该方法涉及在网格步长为H的粗网格上解一个Stokes特征值问题,在网格步长为h=O(H2)的细网格上解一个Stokes问题．这样使其能够仍旧保持最优的逼近精度,求得的解和一般的稳定化有限元解具有相同的收敛阶,即直接在网格步长为h的细网格上解一个Stokes特征值问题．因此,该方法能够节省大量的计算时间．数值试验验证了理论结果．
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| 关 键 词： | Stokes特征值问题 稳定化方法 最低等阶元 两水平方法 |
| 收稿时间： | 2011-05-04 |
A Two-Level Stabilized Finite Element Method for the Stokes Eigenvalue Problem |
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| HUANG Peng-zhan
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HE Yin-nian
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FENG Xin-long.A Two-Level Stabilized Finite Element Method for the Stokes Eigenvalue Problem[J].Applied Mathematics and Mechanics,2012,33(5):588-597. |
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| Authors: | HUANG Peng-zhan HE Yin-nian FENG Xin-long |
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| Institution: | 1College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P.R.China;2Center for Computational Geosciences, School of Mathematics and Statistics, Xi′an Jiaotong University, Xi’an 710049, P.R.China |
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| Abstract: | A two-level stabilized finite element method for the Stokes eigenvalue problem based on local Gauss integration was considered.The method involved solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h=O(H2),which can still maintain an asymptotically optimal accuracy.The given method provided an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution,which involved solving a Stokes eigenvalue problem on a fine mesh with mesh size h.Hence,the method can save a large amount of computational time.Moreover,numerical tests confirmed the theoretical results of the presented method. |
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| Keywords: | Stokes eigenvalue problem stabilized method lowest equal-order pair two-level method |
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