[dune-fem] Direct sum of spaces

[Agnese, Marco]

Hi Martin,
the tuple space is a sort of solution but it is not what I would like. Indeed with the tuple space you have "independent" spaces. 
I use them for example to solve a stokes problem where one space represent the velocity and the other represent the pressure. 

The problem for the direct sum is the following. 
Suppose that you have all your code working with a space P0 therefore you have all your assemble routines, interpolations, errors estimation, dumping and so on. Than you can change the space to another with a simple typedef, so for example you can solve everything for P1. 
Now if you want to use a direct sum of the 2 spaces (P1+P0) you cannot simple define a tuple space of the two spaces P1 and P0 and solve everything over this space. Indeed you have to write a proper assemble routine to handle the tuple space, you have to interpolate the functions in a different way and so on. In other word you have to rewrite big portion of the code breaking the possibility to switch between spaces easily. 

Therefore the tuple space is a wrapper to encapsulate spaces into one in order to pass everything to a solver, but each space will have its own independence. What I would like, instead, is a simple way to sum the spaces and use this new space as an ordinary space. 

That is my understanding, but if I am wrong, please correct me.

Cheers,
Marco.