[dune-functions] Function space of constant functions

[Christian Engwer]

Hi Simon,

On Wed, Nov 14, 2018 at 02:08:35PM -0500, Simon Praetorius wrote:
> Hi everyone,
> 
> I have recently implemented a minimal function space for dune-functions that
> represents essentially something like span{1}, so a space of constants or of
> constant functions. I wanted to have this in the context of dune-functions
> functionspacebases to embed these constants in a PDE setting. Applications
> include:
> 
> - Neumann problem with integral constraint \int u dx = 0
> - Stokes equation with constraint on the pressure (similar to point 1)
> - Coupling of scalar equations involving integral terms with a PDE (e.g.
> Cahn-Hilliard SAV scheme)
> - ...
> 
> See https://gitlab.mn.tu-dresden.de/spraetor/dune-scalarbasis
> 
> Maybe someone is interested in this. Probably there are also other ways to
> achieve the same, but this was for me just an experiment how to include this
> in the functionspacebases setting.
> 
> If there is wider interest in this feature, I could merge this into the
> dune-function repository.

in general I'd say every new functionspacesbasis is a good thing. Yet
I'm not sure that this approach is a good design decision.

At least for the first two points I'd rather think your discretization
needs something to include constraints based on functionals?!
Regarding the Cahn-Hilliard example I don't this model, so I can't
judge. I found an arxiv articel on this scheme, but it was unclear for
me, where your global value comes into play. Can you perhaps elaborate
on this?

Best
Christian