[Getfem-users] RT0 and Nedelec vs. Whitney 1 and 2-forms

[Torquil Macdonald Sørensen]

Hi!

I'm having trouble with calculation of mass matrix elements on a 3d tetrahedron 
mesh. I have two different cases. In the first case I want to use Whitney 1-form 
edge elements, and in the second case Whitney 2-form face elements. I'm given to 
understand that these are the same as the NEDELEC and RT0 elements offered by 
GetFEM.

The Whitney elements are defined as follows: For a point i, lambda_i is the 
usual affine function that is equal to 1 at i, and equal to zero at neighbouring 
points.

For an edge {ij} going from point i to point j, the Whitney 1-form element is

lambda_ij := lambda_i grad lambda_j  - lambda_j grad lambda_i

The "2-form" element for a face {ijk} is

lambda_{ijk} := 0.5*(lambda_i (grad lambda_j) x (grad lambda_k) + cyclic 
permutations of {ijk}).

When varying the "fineness"/lattice spacing of the mesh for a given physical 
domain [0,1]^3, these definitions lead to the following behaviour of the mass 
matrix components:

m_ff' ~ 1/h

m_ee' ~ h

where m_ff' is a component of the mass matrix for the 2-form elements, m_ee' is 
the same for the 1-form elements, and h is the lattice spacing.

However, in my case, the components m_ff' decreases when h decreases. Does this 
indicate a difference between the definition of the RT0 element relative to the 
Whitney 2-form element? If so, is it possible to get one from the other by a 
simple multiplication by h?

Thanks
Torquil