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Journal of Zhejiang University SCIENCE A 2001 Vol.2 No.2 P.165~169

http://doi.org/10.1631/jzus.2001.0165


FINITE VOLUME METHOD BASED ON THE CROUZEIX-RAVIART ELEMENT FOR THE STOKES EQUATION


Author(s):  LI Da-ming

Affiliation(s):  Dept. of Mathmatics, Zhejiang University, Hangzhou 310027, China

Corresponding email(s): 

Key Words:  Stokes equation, finite volume method, Crouzeix-Raviart element


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LI Da-ming. FINITE VOLUME METHOD BASED ON THE CROUZEIX-RAVIART ELEMENT FOR THE STOKES EQUATION[J]. Journal of Zhejiang University Science A, 2001, 2(2): 165~169.

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Abstract: 
The author provides a new discretization method-the finite volume method(FVM). For the stokes equation the velocity space is approximated by the nonconforming linear element based on the dual partition and the pressure by the piecewise constant based on the primal triangulation. Under the suitable smoothness of the solution, the optimal convergence rate O(h) is obtained, where h denotes the parameter of the space discretization.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Chatzipanteliols Panagiotis, 1993. A finite volume method based on the Crouzix-Raviart element for the elliptic PDE's in two dimension. Numer.math. 82: 409-432.

[2] Chou S.H., 1998. A covolume element method based on rotated bilinears for the general stokes problem.SIAM.J.Anal.33(2): 499-507.

[3] Chou, S.H., 1997. Analysis and convergence of a MAC-like scheme for the generali-zed stokes problem. Numer.method for PDE.13: 147-162.

[4] Li Cai., Song Wang, 1993. The finite volume method and application in combination. Jour of Comp and Appli Math.106: 21-53.

[5] Mishev Liya, D., 1999. Finite Volume Element methods for non-definite problem.Numer.math. 83: 162-175.

[6] Vanselow Reiner, 1998. Convergence analysis of a finite volume method via a new nonconforming finite element method. Numer method for partial diff equ.14: 213-231.

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