Volume 2, Issue 1
Two-Level Methods Based on three Corrections for the 2D/3D Steady Navier-Stokes Equations

C. Wen & T.-Z. Huang

Int. J. Numer. Anal. Mod. B, 2 (2011), pp. 42-56

Published online: 2011-02

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  • Abstract
Two-level finite element methods are applied to solve numerically the 2D ⁄ 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.
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65N30 76M10

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COPYRIGHT: © Global Science Press

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@Article{IJNAMB-2-42, author = {C. Wen and T.-Z. Huang}, title = {Two-Level Methods Based on three Corrections for the 2D/3D Steady Navier-Stokes Equations}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2011}, volume = {2}, number = {1}, pages = {42--56}, abstract = {Two-level finite element methods are applied to solve numerically the 2D ⁄ 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.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/298.html} }
TY - JOUR T1 - Two-Level Methods Based on three Corrections for the 2D/3D Steady Navier-Stokes Equations AU - C. Wen & T.-Z. Huang 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 ⁄ 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.
C. Wen and T.-Z. Huang. (2011). Two-Level Methods Based on three Corrections for the 2D/3D Steady Navier-Stokes Equations. International Journal of Numerical Analysis Modeling Series B. 2 (1). 42-56. doi:
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