Hello Johannes,
in your code you compute the integral of the shape functions. For most
finite elements (including the FE_Q) this has nothing to do with the dof
values.
Best Regards,
Markus
Am 13.07.11 12:29, schrieb Johannes Reinhardt:
Hello,
I want to use parts of deal.ii to work with a problem which does not
impose any constraints on the boundary. However, I run into some
problems with boundary dofs and do not see a way to properly solve them.
I am using deali.ii 6.3.1.
The attached code serves to illustrate my problem. It was my first
attempt to calculate the discretised representation of a 2D function
(the constant function in this case), and output it. The result however
is not what I want. It is not constant and at the boundaries the value
of the reconstructed function is too small. I believe this is the case,
because there are contributions to the value of the boundary dofs are
implicitly zero, as the cells for these contributions are not existing.
Or posed differently, it is a problem of normalisation, as the boundary
dof shape functions have a smaller support (only one quarter for a dof
in a corner, one half for a dof on a edge of the domain).
I guess that this is usually not a problem, when one uses Dirichlet or
Neumann boundary conditions, where the values for these dofs are fixed.
My idea of a solution would be to scale the contributions to boundary
cells by a factor to compensate for the wrong normalisation. But I do
not see how to determine this factor reliably and for all dimensions. I
have to find out for all the boundary dofs (which I can obtain with
DoFTools::extract_dofs_with_support_on_boundary) how many contributing
cells are missing. What is an appropriate way to do that?
Thank you in advance
Regards
Johannes Reinhardt
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