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[Robert C. Kirby <kirby@xxxxxxxxxxxx>]

I would suggest that this is too complicated.
We don't need to know the kind of dof to do this

There are two kinds of mappings from functions into function spaces we 
want to consider
i.) The L2 projection
ii.) The nodal interpolant

In order to do the first, we just need the function to be callable -- 
we tabulate at quadrature points and compute (f,phi) for every member 
of the nodal basis.  The dof map matters to piece this together.

In order to do the second, we need the ability to apply our linear 
functionals to the function in consideration.  In the old version of 
FIAT, this was no big deal.  In the new version, every function is a 
polynomial and hence a vector, while every functional is also a vector 
so that it may be applied on the appropriate space by dot product.  I'm 
not sure how to get the real nodal interpolant.  Perhaps I could add a 
feature to functionals so that they could be applied to callable 
objects as well as to polynomials?

In order to get the nodal interpolant on one element, you need
I(f) = n_i(f) \psi_i

where \psi_i is the nodal basis and n_i are the nodes.

On May 11, 2005, at 5:37 PM, Anders Logg wrote:

> Now that the generation of dof-maps is (mostly) in place in FFC, the
> next thing we need to fix is the projection (interpolation) of
> user-defined functions onto the finite element space. (The third step
> will be evaluation at vertices for post-processing.)
>
> I then need to take a node in FIAT and ask for its coordinate (if the
> dual basis is point evaluation). The coordinate I get would then be
> mapped from the reference element to the physical element where the
> user-defined function is evaluated to obtain its expansion in the
> basis.
>
> I could generate this from what I have now, but I also need
> coordinates of internal dofs.
>
> Maybe in the future, we might want to do something more general, like
> projecting onto the Dubiner basis and doing a linear transformation to
> get the expansion at run-time?
>
> /Anders
>
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