I'm solving a 2D problem on quadrilateral cartesian mesh using FE_Q(1)
> elements.
> I would like to compute the gradient of the bilinear solution, known to
> belong to the FE_Nedelec(0) space: how can I manage to do it?
>
For visualizing the gradient of discrete solution, you have multiple
options.
If you are using FE_Q(1) elements most visualization tools, should be able
to give you an exact representation of your discrete solution.
In Paraview, for example, you could just use the filter "Gradient of
Unstructured DataSet".
Another way would be to use DataPostprocessor [1]. Have a look at
step-29[2] for how to use it.
> In particular I'm only interested in computing the tangential component of
> the gradient on each mesh face, but I don't really know (and can't find
> anything on the documentation) how to approach the problem of building a
> gradient vector associated with the Nédélec degrees of freedom.
>
What do you actually want to do with the tangential gradients at the faces?
Is visualizing sufficient for you or do you really want to compute a
projection into the FE_Nedelec(0) space?
Best,
Daniel
[1] https://www.dealii.org/8.4.0/doxygen/deal.II/classDataPostprocessor.html
[2] https://www.dealii.org/8.4.0/doxygen/deal.II/step_29.html
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