Thanks to both of you guys for answering my question. I really appreciate the response. This clears things up.
Dan On Fri, Jul 29, 2011 at 4:32 PM, Guido Kanschat <[email protected]> wrote: > 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<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 >>> >> ______________________________**_________________ >> dealii mailing list >> http://poisson.dealii.org/**mailman/listinfo/dealii<http://poisson.dealii.org/mailman/listinfo/dealii> >> > > ______________________________**_________________ > dealii mailing list > http://poisson.dealii.org/**mailman/listinfo/dealii<http://poisson.dealii.org/mailman/listinfo/dealii> >
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