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
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