Re: [deal.II] Question about postprocessing

[Wolfgang Bangerth]

Konrad,

> I also have a little question about postprocessing in different spaces.
> I am post processing two solutions of the same problem but solved in two
> different (pairs of) spaces. One quantity, for example, is called u and
> is either in H(curl) or in H(div) depending on the form of the problem.
> Another is sigma and it is either in H^1 or in H(curl), respectively.
>
> I need to compute things that involve the divergence of u when u is in
> H(div) or the curl when u is in H(curl). Both things I do using the
> DataPostprocessor class with entries of the (matrix valued) gradient of
> u but I don't know the internals.

This seems like the appropriate approach. DataPostprocessor evaluates
the gradient of the solution at certain points on each cell and you get
to use that to compute the divergence or curl of the solution -- it's
really just a linear combination of the elements of the gradient matrix
like you say.


> My problem ist that when comparing quantities that should be similar
> according to the math then I get differences that are too large
> (intuitively).

Large or small are relative. The question is: Do things converge?


> The thing is that when I have a quantity that is in H(curl) using
> Nedelec approximation then I can nicely take the curl but divergence
> will be zero by construction. Same if u is in H(div) with Raviart-Thomas
> approximation (then the curl is zero by construction).

So then if I interpret things correctly, you are saying that if your
solution is in H(curl), then
div u_h = 0
and consequently
div u_h does not converge to div u
or equivalent,
||div(u-u_h)|| --/--> 0

Is this your worry? Do you have any evidence that it *should* converge
to zero?

Best
W.


--
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Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/