An Inf-Sup Stabilized Finite Element Method by Multiscale Functions for the Stokes Equations
Zhihao Ge 1*, Yinnian He 2, Lingyu Song 31 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
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, 35K60
Key words: Stabilized finite element method; multiscale functions; Petrov-Galerkin approach; inf-sup condition.
Email: email@example.com (Z. Ge), firstname.lastname@example.org (Y. He), email@example.com (L. Song)