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Adv. Appl. Math. Mech., 1 (2009), pp. 273-287. |
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An Inf-Sup Stabilized Finite Element Method by Multiscale Functions for the Stokes Equations Zhihao Ge 1*, Yinnian He 2, Lingyu Song 3 1 School of Mathematics and Information Science, Henan University, Kaifeng 475001, P.R. China.2 School of Science, Xi'an Jiaotong University, Xi'an 710049, P.R. China. 3 School of Science, Chang'an University, Xia'an 710064, P.R. China. Received 15 November 2008; Accepted (in revised version) 16 January 2009 Abstract In the paper, an inf-sup stabilized finite element method by multiscale functions for the Stokes equations is discussed. The key idea is to use a Petrov- Galerkin approach based on the enrichment of the standard polynomial space for the velocity component with multiscale functions. The inf-sup condition for P1-P0 triangular element (or Q1-P0 quadrilateral element) is established. And the optimal error estimates of the stabilized finite element method for the Stokes equations are obtained. AMS subject classifications: 76D05, 65N30, 35K60Key words: Stabilized finite element method; multiscale functions; Petrov-Galerkin approach; inf-sup condition. *Corresponding author. Email: zhihaoge@gmail.com (Z. Ge), heyn@mail.xjtu.edu.cn (Y. He), sly20050602@163.com (L. Song) |