Volume 12, Issue 3
Comparative Study of Space Iteration Methods Based on Nonconforming Finite Element for Stationary Navier-Stokes Equations

East Asian J. Appl. Math., 12 (2022), pp. 628-648.

Published online: 2022-04

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• Abstract

Steady Navier-Stokes equations are solved by three different space iteration methods based on the lowest order nonconforming finite element pairs $\mathscr{P}_1\mathscr{N} \mathscr{C}-\mathscr{P}_1,$ including simple, Oseen, and Newton iterative methods. The stability and convergence of these methods are studied, and their CPU time and numerical convergence rate are discussed. Numerical results are in good agreement with theoretical findings. In particular, numerical experiments show that for large viscosity, the Newton method converges faster than to others, whereas the Oseen method is more suitable for the equations with small viscosity.

• Keywords

Navier-Stokes equations, nonconforming finite element, space iterative method, stability and convergence.

35L70, 65N30, 76D06

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@Article{EAJAM-12-628, author = {}, title = {Comparative Study of Space Iteration Methods Based on Nonconforming Finite Element for Stationary Navier-Stokes Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2022}, volume = {12}, number = {3}, pages = {628--648}, abstract = {

Steady Navier-Stokes equations are solved by three different space iteration methods based on the lowest order nonconforming finite element pairs $\mathscr{P}_1\mathscr{N} \mathscr{C}-\mathscr{P}_1,$ including simple, Oseen, and Newton iterative methods. The stability and convergence of these methods are studied, and their CPU time and numerical convergence rate are discussed. Numerical results are in good agreement with theoretical findings. In particular, numerical experiments show that for large viscosity, the Newton method converges faster than to others, whereas the Oseen method is more suitable for the equations with small viscosity.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.300121.261221 }, url = {http://global-sci.org/intro/article_detail/eajam/20411.html} }
TY - JOUR T1 - Comparative Study of Space Iteration Methods Based on Nonconforming Finite Element for Stationary Navier-Stokes Equations JO - East Asian Journal on Applied Mathematics VL - 3 SP - 628 EP - 648 PY - 2022 DA - 2022/04 SN - 12 DO - http://doi.org/10.4208/eajam.300121.261221 UR - https://global-sci.org/intro/article_detail/eajam/20411.html KW - Navier-Stokes equations, nonconforming finite element, space iterative method, stability and convergence. AB -

Steady Navier-Stokes equations are solved by three different space iteration methods based on the lowest order nonconforming finite element pairs $\mathscr{P}_1\mathscr{N} \mathscr{C}-\mathscr{P}_1,$ including simple, Oseen, and Newton iterative methods. The stability and convergence of these methods are studied, and their CPU time and numerical convergence rate are discussed. Numerical results are in good agreement with theoretical findings. In particular, numerical experiments show that for large viscosity, the Newton method converges faster than to others, whereas the Oseen method is more suitable for the equations with small viscosity.

Jiawei Gao & Jian Li. (2022). Comparative Study of Space Iteration Methods Based on Nonconforming Finite Element for Stationary Navier-Stokes Equations. East Asian Journal on Applied Mathematics. 12 (3). 628-648. doi:10.4208/eajam.300121.261221
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