On 4/18/21 10:50 PM, John Smith wrote:
Then I have fed this solution together with the dof handler to the
VectorTools::point_value on a grid of regularly spaced points. The results
were written into a *.csv file. Then I have made the vector plot out of it.
The 0-th order, FE_Nedelec<2> fe(0), looks just as what I would expect. The
2-nd order, however, looks just like the 0-th order. I opened the files in
spreadsheet and indeed – the shape functions of the 0-th and 2-nd order are
the same. I ruled out the possibility of mistake (the program prints
fe.degree) and began worrying. I think VectorTools::point_value is to blame
probably…
Is there a replacement for it?
You too quickly jump to the conclusion that the function you called must have
a bug. While that's not impossible, you should first run more tests.
All you have shown is that the very first of the shape functions of
FE_Nedelec(0) may be the same as the very first shape function of
FE_Nedelec(1). But is this really the case? And even if that were so, would
that constitute a bug?
For the first question, when you use DataOut to output a finite element field,
remember that all you get is a piecewise linear representation of the field.
Take a look at the documentation of DataOut::build_patches() to see one would
get a more accurate representation.
For the second question: All you need is that the shape functions for higher
polynomial degrees are linearly independent of the ones for lower polynomial
degrees. While it is true that, for example, for the FE_Q(2) element *all*
shape functions are different from the ones of FE_Q(1), this is not a
requirement. Take a look at FE_QHierarchical, for example. I don't recall
which approach FE_Nedelec takes, but it is at least conceivable that it has
the same hierarchical structure.
Best
W.
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Wolfgang Bangerth email: [email protected]
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