# Two-level method based on Newton iteration for the stationary Navier-Stokes Equations

## Keywords:

Navier-Stokes equations, equal-order pair, Newton iteration, Local Gauss integration, Two-level strategy## Abstract

This paper propose and analyze the two-level stabilized finite element method for the stationary Navier-Stokes equations based on Newon iteration. This algorithm involves solving one small, nonlinear coarse mesh with mesh size H and two linear problems on the fine mesh with mesh size h. Based on local Gauss integration and the quadratic equal-order triangular element ,the two-level stabilized method our study provide an approximate solution with convergence rate of same order as the approximate solution ofÂ one-level method,which involves solving one large Navier-Stokes problem on a fine mesh with mesh size h. Hence,our method can save a large amount of computational time. Finally,some numerical tests confirm the theoretical expectations.

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*Asian Journal of Fuzzy and Applied Mathematics*,

*1*(4). Retrieved from https://ajouronline.com/index.php/AJFAM/article/view/762

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