Abstract
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 Q1−P0 quadrilateral element and the P1−P0 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.
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He, Y., Wang, A. & Mei, L. Stabilized finite-element method for the stationary Navier-Stokes equations. J Eng Math 51, 367–380 (2005). https://doi.org/10.1007/s10665-004-3718-5
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DOI: https://doi.org/10.1007/s10665-004-3718-5