Journal of Engineering Mathematics

, Volume 51, Issue 4, pp 367–380

Stabilized finite-element method for the stationary Navier-Stokes equations



A stabilized finite-element method for the two-dimensional stationary incompressible Navier-Stokes equations is investigated in this work. A macroelement condition is introduced for constructing the local stabilized formulation of the stationary Navier-Stokes equations. By satisfying this condition, the stability of the Q1P0 quadrilateral element and the P1P0 triangular element are established. Moreover, the well-posedness and the optimal error estimate of the stabilized finite-element method for the stationary Navier-Stokes equations are obtained. Finally, some numerical tests to confirm the theoretical results of the stabilized finite-element method are provided.


error estimation Navier-Stokes equations stabilized finite element 


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© Springer 2005

Authors and Affiliations

  1. 1.Faculty of Science (State Key Laboratory of Multiphase Flow in Power Engineering)Xi’an Jiaotong UniversityXi’anP.R. China
  2. 2.School of Basic CoursesBeijing Institute of MachineryBeijingP.R. China
  3. 3.Faculty of ScienceXi’an Jiaotong UniversityXi’anP.R. China

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