Dear all,

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

Regards

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 hereďĽź Thanks!

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I have a question with respect to â€śBDF 3 schema for the time integrationâ€ť.

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 havenâ€™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 wrongâ€¦

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.