[Dune] Lagrange local basis on pyramids, in dune-localfunctions

[Simon Praetorius]

Hello,
While implementing the partial() method in dune-localfunction for 
several localBasis, I came across the pyramid basis functions. Those are 
implemented as piecewise linear/quadratic functions and I want to ask: why?

For me, the natural way would be to implement it as bilinear/biquadratic 
x linear/quadratic. The drawback is, that the polynomial order then 
increases, but to be exact, the polynomial order 1, as given currently 
for the pyramidp1 localBasis would only be enough for quadrature 
formulas, if the quadrature is also implemented piecewise over the 
sub-tetrehedra and then added up.

The combination of the current pyramid elements with hexahedral Qk 
elements would also not fit perfectly.

In contrast to this, the prism elements are implemented as bilinear x 
linear functions and thus work well.

Have I missed something, e.g. is the smooth pyramid element implemented 
in some other class that I have overseen?

I would suggest to either replace the current pyramid element with the 
smooth ones, or add another pyramid finite element additionally if the 
piecewise smooth elements are in use somewhere.
The evaluateJacobian test in the test-localfe implementation could then 
also test for the pyramid elements instead of removing the test for only 
these elements.

Simon Praetorius