# Convergence varying for Newtons Method

**URL:** <https://community.freefem.org/t/convergence-varying-for-newtons-method/1406>\
**Category:** General Discussion\
**Created:** [January 3, 2022, 6:22am UTC](https://community.freefem.org/t/convergence-varying-for-newtons-method/1406 "2022-01-03T06:22:37Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![sumantkr](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/sumantkr/32/2681_2.png) [@sumantkr](https://community.freefem.org/u/sumantkr)\
**Post date:** [January 3, 2022, 6:22am UTC](https://community.freefem.org/t/convergence-varying-for-newtons-method/1406/1 "2022-01-03T06:22:37Z")

</div>

Dear All, Anyone has working experience with the NS method mentioned in the ( [Navier-Stokes](https://doc.freefem.org/tutorials/navierStokesNewton.html#newton-method-for-the-steady-navier-stokes-equations)).

My solution is not converging for this approach.

---

<div class="post-metadata">

**Author:** ![zhaog6](https://avatars.discourse-cdn.com/v4/letter/z/4af34b/32.png) [@zhaog6](https://community.freefem.org/u/zhaog6)\
**Post date:** [January 12, 2022, 1:48am UTC](https://community.freefem.org/t/convergence-varying-for-newtons-method/1406/2 "2022-01-12T01:48:25Z")

</div>

I used Newton method to solve NS equations (2-D driven-cavity flow) in FreeFem++ (old FreeFEM), but it was 4 years ago. If your coefficient matrix and right-hand side assembled are correct, generally, the nonlinear convergence problem may be caused by a very large Reynolds number.  
As suggested in the example, you can use the strategy of continuous vanishing viscosity, and you can add some stabilization methods such as SUPG/PSPG, GLS etc. (practically, it can simulate 0.5~1 Million Reynolds number, but unfortunately, it is not a physical solution in this case). Algebraically, you can also refer to Augmented Lagrangian preconditioner in [GitHub - prj-/moulin2019al: Augmented Lagrangian Preconditioner for Hydrodynamic Stability Analysis](https://github.com/prj-/moulin2019al) by Pierre, Johann, Olivier.  
In addition, using PETSc/SNES for nonlinear iteration is also recommended because more robust.

---

<div class="post-metadata">

**Author:** ![sumantkr](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/sumantkr/32/2681_2.png) [@sumantkr](https://community.freefem.org/u/sumantkr)\
**Post date:** [January 13, 2022, 8:40am UTC](https://community.freefem.org/t/convergence-varying-for-newtons-method/1406/3 "2022-01-13T08:40:24Z")

</div>

Thanks, @zhaog6 Sir. It is really helpful.