Stabilized finite element method for the non-stationary
Yinnian He - Faculty of Science, Xi'an Jiaotong University, Xi'an 710049, China (email)
Abstract: In this article, a locally stabilized finite element formulation of the two-dimensional Navier-Stokes problem is used. A macroelement condition which provides the stability of the $Q_1-P_0$ quadrilateral element and the $P_1-P_0$ triangular element is introduced. Moreover, the $H^1$ and $L^2$-error estimates of optimal order for finite element solution $(u_h,p_h)$ are analyzed. Finally, a uniform $H^1$ and $L^2$-error estimates of optimal order for finite element solution $(u_h,p_h)$ is obtained if the uniqueness condition is satisfied.
Keywords: Navier-Stokes problem, stabilized finite element, uniform error
Received: April 2005; Revised: September 2005; Published: October 2005.
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