Joshua,
first, thanks for writing this code. Second: I've committed it to our 
subversion repository, with a few minor edits and split into a .cc and 
a .h file. Third, I've already fixed a couple of assertions you hit in 
your code that had to do with interfacing the FE_Nothing with FE_Q.

Now for the rest: I've modified your little test program into a program for 
our testsuite. Can I ask you to read through the "Regression tests" 
section of this page:
  http://www.dealii.org/developer/development/testsuite.html
If you check out the testsuite from svn (along with the current version of 
the library proper) you'll find your program as hp/fe_nothing_01.cc. It 
still fails, but at a later point from where it stopped for you -- in 
FiniteElement::compare_for_face_domination, a function that you also need 
to overload in FE_Nothing. Face domination is a concept that is explained 
in a bit detail in 
  http://www.math.tamu.edu/~bangerth/publications/2006-hp.pdf
In essence, in the implementation of this function you'll have to say 
whether the FE_Q or the FE_Nothing is the master -- a decision the 
implementations in the two classes have to agree upon as they both could 
be asked this question. In FE_Q I've picked the FE_Q as the master, so 
you'll have to do the same in FE_Nothing.

See how far you'll get after implementing this function and let me know 
when you don't know any further again!

Again, thanks for working on this!
 Wolfgang

PS: When you have time, would you mind copying (and if necessary 
augmenting) the comments for all the functions in FE_Nothing from 
FiniteElement so they would show up in the documentation pages for 
FE_Nothing?

-- 
-------------------------------------------------------------------------
Wolfgang Bangerth                email:            [email protected]
                                 www: http://www.math.tamu.edu/~bangerth/

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