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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