Enriched spaces for PEERS: help on implementation

Question

I am trying to enrich the Raviart-Thomas space with a bubble element's curl:

from dolfin import *

B = TensorFunctionSpace(mesh, "Bubble", 3)
_H = VectorFunctionSpace(mesh, 'RT', 1)

H = _H+curl(B)

Which does not work. I would appreciate any help for this. What I am trying to implement is the PEERS base, which approximates tensor spaces with RT enriched with the curl of a bubble function. Another way of implementing this would be to add the Bubble space to the MixedSpace and the just add the curl in each part where it corresponds, but I believe there has to be a more elegant and comprehensive way.

Thanks

Answer 1

You need to use

B = VectorFunctionSpace(mesh, "Bubble", 3)

instead of tensor function space. Your _H is vector of vector elements, so it is a tensor element. Since curl(B) is a tensor, the addition is well-defined now.

Comments

Thanks for the correction. With that it is indeed possible to implement both elements separately and afterwards process everything in something like replacing t in _H by t+b, where b is a bubble function. It would be good to know if it is possible to do this more naturally, which would be to have a 'PEERS' element, instead of doing this artificial correction. Apparently not, and anyway thanks again.