Hi Daniel,
right now I don't have to take a look at your slides. So my suggestions
would be:
-Try to implement boundary conditions using Nitsche in your weak
formulation.
-If you have an element that has a midpoint, you would have to write a
new function that interpolates the boundary values. This is what I did for
th C^1 and Adini element.
If you have further questions, please let me know.
Bärbel
--
Bärbel Janssen
Institut für Angewandte Mathematik
Universität Heidelberg
Im Neuenheimer Feld 293, Raum 213
Telefon: +49 6221 54-5449
On Thu, 23 Jun 2011, Daniel Brauss wrote:
Hi Wolfgang and everybody,
I am trying to combine the previous e-mails into one. I have attached
3 slides from a slideshow for the MHD equations and the linear form.
I had some trouble sending the pdf version since it was too big, so I
have attached the tex version (it should compile with PDFLatex).
The Nedelec element used is for the current J. I had written earlier
about Hermite elements, but with the help of my professor found that
the Nedelec elements would work. In the strong form shown in the
slides, J . n = Jext . n is a boundary condition. We are given Jext.
>From reading through Anna Schneebeli's paper, I understand that
the shape functions don't really have support points. Thus
setting boundary conditions for Nedelec elements would
be different from settting the boundary conditions for Lagrangian elements.
I was wondering how boundary conditions could be set for a variable
associated with a Nedelec element. In the other e-mail you mentioned
Baerbel Janssen working with Hermite-type elements. I was thinking
about a simple linear Hermite element on an interval, where the
degrees of freedom are defined using the value and
the derivative at the midpoint. How would someone set the boundary
conditions for this element, if it has only the midpoint as a "support"
point.
Along these lines, I noticed the interpolate function in the Nedelec
documentation
It refers to generalized support points. I guess that these are the quadrature
points where the dof integrals were evaluated? I was wondering how this
function has been used?
Finally, letting x = "generalized support point", I was wondering if it would
make any sense to put in a constraint matrix
a form of "J(x) . n(x) = sum_{k=1} J_{k} phi_{k}(x) . n(x) = boundary_value".
Where k runs through the Nedelec shape functions phi_{k}, and J_{k}
are the solution coefficients. Thanks for everyone's time.
Dan
On Wed, Jun 22, 2011 at 10:03 PM, Wolfgang Bangerth <[email protected]>
wrote:
> For the boundary condition, I have to specify the normal component of
> vector shape functions at the boundary
> [...]
> I am using Nedelec elements for these shape functions.
These two things don't really go well together I believe. The Nedelec element
ensures that the tangential component of solutions are continuous across
faces, but not the normal component. Consequently, there is no way to easily
enforce anything for the normal component of the solution at the boundary. Can
you tell us what your bilinear form?
(The typical use case for Nedelec elements is the curl-curl operator. If you
multiply with a test function and integrate by parts, you'll get boundary
terms as always, but none of the factors in these boundary terms have anything
to do with the normal component of the variable, which also indicates that you
can't impose anything on the normal component of the solution.)
Best
W.
-------------------------------------------------------------------------
Wolfgang Bangerth email: [email protected]
www: http://www.math.tamu.edu/~bangerth/
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