[Getfem-users] Nedelec DOF definition

[Torquil Macdonald Sørensen]

Hi!

While working with FEM_NEDELEC(3), I got some unexpected basis function
values and mass matrix values. I'm used to the Nedelec basis function
definition

sigma_{ij} := lambda_i Grad lambda_j - lambda_j Grad lambda_i

where ij is the line going from node i to node j.

But when I evaluate the FEM_NEDELEC(3) basis function values, I get a
sqrt(2) factor difference between Getfem and my own calculations, for
the DOFs that correspond to local DOF numbers 3,4,5 in the reference
simplex, i.e. those corresponding to edges of length sqrt(2):

I created a mesh consisting of a single simplex with vertices (0,0,0),
(1,0,0), (0,1,0), (0,0,1). The position of DOF 0 is (0.5,0,0). Then I
evaluated the values of all DOFs at this position. According to Getfem,
the value of DOF 3 at this position is (0, sqrt(2), 0). But my own
calculations on paper with the above definition gives (0, 0.5, 0).

Does that mean that Getfem is using additional prefactor in the
definition of the NEDELEC DOFs, that depends on the edge length? I don't
see any such factor in P1_nedelec_::P1_nedelec_(dim_type nc_), but
perhaps it has something to do with what happens in
P1_nedelec_::mat_trans()?

Best regards
Torquil Sørensen