[deal.II] Best approach for multi-variable system with multiple grids

['Maxi Miller' via deal.II User Group]

I have a coupled system of two equations:


<https://lh3.googleusercontent.com/-fYHJLaOgktQ/WWTe-HTVSPI/AAAAAAAACNM/RlbN1Hg0idQceRc0Ww52v34vBZ7ftfAygCLcBGAs/s1600/Screenshot_20170711_111406.png>

<https://lh3.googleusercontent.com/-fYHJLaOgktQ/WWTe-HTVSPI/AAAAAAAACNM/RlbN1Hg0idQceRc0Ww52v34vBZ7ftfAygCLcBGAs/s1600/Screenshot_20170711_111406.png>
<https://lh3.googleusercontent.com/-fYHJLaOgktQ/WWTe-HTVSPI/AAAAAAAACNM/RlbN1Hg0idQceRc0Ww52v34vBZ7ftfAygCLcBGAs/s1600/Screenshot_20170711_111406.png>


which I want to solve. Here k_L, k_E, f_1 and f_2 are nonlinear functions 
depending on T_E and T_L, while Q_E is a nonlinear function depending on 
the time. Now I can either reformulate it as seen in example 33, but then 
have to extend the grids to two grids, not only one (for TE and TL):

>
>
<https://lh3.googleusercontent.com/-9sx7WrIVaEo/WWTfA2mCbtI/AAAAAAAACNQ/_qXwWH5n7wMgrT-4xbPuYLqBYg0QxUudACLcBGAs/s1600/modified_func.png>

or I can do the same approach as in example 28 (where I already have two 
grids), but there the variables L and F are set to zero (only X is 
nonzero). Which of those two approaches is more beneficial for me 
(especcially after I would like to extend it afterwards to two additional 
equations? Or is there another approach I did not consider yet?

The target application is in 3d, and isotrop.

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