Help with modifying step-26 for non-linear part and semi-implicit time-stepping in FEM

[Zoe]

Hi everyone,

I hope you all had a great summer!

My name is Zoe, and I am new to deal.II. I’m currently working on a project where I need to solve a non-linear PDE using semi-implicit time-stepping with the Finite Element Method (FEM). I would like to use deal.II for this purpose.

PDE:

semi-implicit:

After going through step-26, I’ve learned how to implement time-stepping using the theta-scheme. However, I’m struggling to adapt the existing code to incorporate semi-implicit time-stepping and non-linear parts for my problem. 

Could anyone provide guidance on how to modify step-26 or suggest alternative steps/examples that might be more suitable for this type of problem?

I would greatly appreciate any suggestions or references to relevant examples within the deal.II documentation or tutorials.

Thank you very much for your time and assistance!

Best regards,

Zoe

[Wolfgang Bangerth]

> My name is Zoe, and I am new to deal.II. I’m currently working on a
> project where I need to solve a non-linear PDE using semi-implicit
> time-stepping with the Finite Element Method (FEM). I would like to use
> deal.II for this purpose.
>
> PDE:
>

> Screenshot 2024-09-26 at 16.51.14.png
>
> semi-implicit:
>

> Screenshot 2024-09-26 at 16.51.26.png
>
> After going through step-26, I’ve learned how to implement time-stepping
> using the theta-scheme. However, I’m struggling to adapt the existing
> code to incorporate semi-implicit time-stepping and non-linear parts for
> my problem.
>
> Could anyone provide guidance on how to modify step-26 or suggest
> alternative steps/examples that might be more suitable for this type of
> problem?

Zoe:
I think you will find yourself interested in this code gallery program:
https://dealii.org/developer/doxygen/deal.II/code_gallery_Swift_Hohenberg-Solver.html
It essentially does what you want to do, just for a problem with four
(instead of two) spatial derivatives.

Best
W.