Non linear time dependent problem

Dear all,

I looking for an or more examples of nonlinear time dependent problem using Newton method or other.

Regards

During the freefem days and all during teaching sessions, I solve of Boussinessq Equation
(Inccompressible Navier Stokes with temperature) to see Rayleigh-Bernard instability.

The Non linear Part is done with Fixe-Point and Newton iteration method,
And I use BDF 3 schema for the time integration.

Rayleigh-Benard-time.edp (3.9 KB)

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if i can have documentation for the PDE equations in this example ?

Would you please add the video link or slides here? Thanks!

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I have a question with respect to “BDF 3 schema for the time integration”.

Can you please elaborate more on this time integration scheme? What is the order of accuracy of this time integration scheme?

have you get through the weak form derivation? I have been in this part weveral days and still haven’t get the same form as in FixePB.

remark, on BDF3 schema to get the correct error leve (o(dt^3) l, you must initialize with schema of order
o(dt^2) because you have no sum for initialization so no problem init BDF1 for the fist set and BDF2 for the second step, and after BF3 , but if you want to go to BDF4 it will be wrong…

Thank you for sharing the code.

The code is a serial code. Is there a parallel version of the code available?

They are no good parallel version to day.