TY - JOUR
T1 - Two-Level Methods Based on three Corrections for the 2D/3D Steady Navier-Stokes Equations
JO - International Journal of Numerical Analysis Modeling Series B
VL - 1
SP - 42
EP - 56
PY - 2011
DA - 2011/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnamb/298.html
KW - Navier-Stokes equations
KW - finite element method
KW - Stokes correction
KW - Oseen correction
KW - Newton correction
KW - two-level method
AB - Two-level finite element methods are applied to solve numerically the 2D &#8260 3D steady
Navier-Stokes equations if a strong uniqueness condition 
(\frac{\|f\|_{-1}}{\|f\|_0})^\frac{1}{2}\leq\delta=1-\frac{N\|F\|_{-1}}{\nu^2} holds,
where N is defined in (2.4)-(2.6). Moreover, one-level finite element method is applied to solve
numerically the 2D/3D steady Navier-Stokes equations if a weak uniqueness condition 
0<\delta<(\frac{\|f\|_{-1}}{\|f\|_0})^\frac{1}{2} holds. The two-level algorithms are motivated by solving 
a nonlinear problem on a coarse grid with mesh size H and computing the Stokes, Oseen and Newton correction on a fine
grid with mesh size h << H. The uniform stability and convergence of these methods with respect
to  and grid sizes h and H are provided. Finally, some numerical tests are made to demonstrate
the effectiveness of one-level method and the three two-level methods.