I guess the documentation is a bit confusing there. What I read is essentially
this:
1. The partial derivatives of FE_Nedelec functions are correct only if the cell
is a parallelogram in 2D or parallelepiped in 3D.
2. The curl of the FE_Nedelec functions is correct on general quadrilaterals,
since the 'wrong' terms cancel
Dan, does that answer your question?
Guido
On 07/28/2011 09:40 AM, Markus Bürg wrote:
Hello Dan,
somehow I do not get your point. An affine mapping is a linear mapping. Thus it
will do the right thing for bilinear mappings in 2d and trilinear mappings in
3d, but for higher order mappings it will introduce some error.
Best Regards,
Markus
Am 28.07.11 16:30, schrieb Daniel Brauss:
Thanks for the reply Markus. I have looked through the link that you mentioned
http://www.dealii.org/developer/doxygen/deal.II/classFE__Nedelec.html
and do not see any mention of trilinear transformations. I do see bilinear
mentioned in the paragraph
"The first reason is that the gradient of the Jacobian vanishes if the cells
are mapped by an affine mapping, to which the usual bilinear mapping reduces
if the cell is a parallelogram. Then the gradient of the shape functions is
computed exact, since the first term is zero."
But this seems to imply that the transformation is again affine (combination
of rotation, scaling, shear, and a translation/shift) as I interpret it as a
shear. So it does not appear that a real bilinear or trilinear transformation
is mentioned, where the jacobian of the element mapping is non-constant. This
kind of situation arises in the torus I am meshing, where I get trilinear
transformations. I cannot seem to get away from this, or would be happy to use
a affine transformation. I guess my question is whether or not something
special has to be done for stiffness matrix integrals having Nedelec shape
functions with trilinear mappings from the reference element to the real
elements?
Thanks,
Dan
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