The Crouzeix-Raviart type nonconforming finite element method for the nonstationary Navier-Stokes equations on anisotropic meshes

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• 作者：Dong-yang Shi (1)
  Hui-min Wang (2)
  
  1. Department of Mathematics ; Zhengzhou University ; Zhengzhou ; 450001 ; China
  2. College of Science ; Henan Institute of Engineering ; Zhengzhou ; 450007 ; China
  
• 关键词：Navier ; Stokes equations ; C ; R type ; nonconforming linear triangular FE ; anisotropic meshes ; error estimates ; 65N30 ; 65N15
• 刊名：Acta Mathematicae Applicatae Sinica, English Series
• 出版年：2014
• 出版时间：March 2014
• 年：2014
• 卷：30
• 期：1
• 页码：145-156
• 全文大小：238 KB
• 参考文献：1. Adams, RA (1975) Sobolev spaces. Academic Press, New York
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  22. Shi, DY, Xu, C (2012) Anisotropic nonconforming Crouzeix-Raviart type FEM for second-order elliptic problems. Appl. Math. Mech. 33: pp. 243-252 CrossRef
  23. Shi, DY, Xu, C (2012) An anisotropic locking-free nonconforming triangular finite element method for planar linear elasticity problem. J. Comput. Math. 30: pp. 124-138 CrossRef
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• 刊物主题：Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics;
• 出版者：Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
• ISSN：1618-3932

文摘

This paper is devoted to study the Crouzeix-Raviart (C-R) type nonconforming linear triangular finite element method (FEM) for the nonstationary Navier-Stokes equations on anisotropic meshes. By introducing auxiliary finite element spaces, the error estimates for the velocity in the L 2-norm and energy norm, as well as for the pressure in the L 2-norm are derived.