Solving a Coupled PDE's using FEniCS

Question

Hello
I am pretty new on FEniCS.and I want to use FEniCS to solve a coupled set of PDE's including 3 different fields. These equations are coupled and should be solved to find three unknowns. I would like to explain my problem briefly.

Firstly I just want to solve these coupled PDE's in one dimension and then extend it to 2-D. Could you please tell me how I can deal with this problem in FEniCS? I would really appreciate you referring me to a solved example similar to my problem so I can come up with an idea to implement it in FEniCS. Thanks in advance for your time and attention.
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Comments

How are you going to couple them in time? Solving for the chemical field simultaneously in the three equations or first solve it in the first equation and then use that value in the other two?

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Hi
Here is the idea:
Chemical and the electrical fields should be solved simultaneously for 2 unknowns:

1- C_alpha
2- Electric potential

And finally the values of C_alpha should be used in the last equation (equation of motion) to find the displacement (u).

I hope I explained it well!

Answer 1

To get a working solver for your problem you can use mixed spaces for the fields you're trying to find.

The latest example of their use (for an advection-diffusion-reaction system of equations) is here:
https://fenicsproject.org/pub/tutorial/html/._ftut1010.html#ftut1:reactionsystem

Then to make a faster solver it might be necessary to solve the equations one a time like in this example:
https://fenicsproject.org/pub/tutorial/html/._ftut1009.html
The advantage of this method is that you can tailor a different linear/non-linear solver for each equation

Answer 2

Look into problems with mixed spaces, such as Navier-stokes.