Hello Dan,
I am not sure, if the elements you suggest really define a proper finite
element space. Perhabs you should go back another step and think in
terms of function spaces first. A function from which space do you want
to approximate? As far as I remember one does not need such exotic
elements for magneto-hydro dymanics, it is usually done by a combination
of H(div)- and H(curl)-conforming finite elements. But I am not an
expert in MHD, so I cannot give you the correct answer right away.
Best Regards,
Markus
Am 24.06.11 15:24, schrieb Daniel Brauss:
Hello all,
Seeing that I am striking out with Nedelec and it appears that this
element
is the only element that satisfies the conditions that I need (except
for the
dofs), I was hoping to ask a couple questions about two other types of
elements that could do the job.
1) The first is an anistropic vector Lagrange element Q_{k-1,k,k} X
Q_{k,k-1,k} X Q_{k,k,k-1}
where k = 2 and the element is discontinuous in the k-1 direction.
It appears that I would only have to
implement a scalar anisotropic Q_{k-1,k,k} element that is
discontinuous in the k-1
direction and then assemble the vector finite element using three
of these.
Are these elements already in use? Wolfgang mentioned that it may
be possible
to implement this type of element as discontinuous at the edges in
all directions
(rather than just the k-1), and use the DG method to solve (if I
understood correctly).
If this seems feasible, is not yet implemented (and hopefully not
too difficult for a
young c++ programmer) I would be willing to do this.
2) The second element that could do the job comes from a scalar 9
node Hermite element.
The nodes are coming from the principal lattice of degree two
(which has 27 points)
Each component of the vector finite element would be one of
these. For the ith vector
component (let's say the x-direction) you get down to 9 nodes by
removing the nodes
that not on faces perpendicular to the ith coordinate axis
(remove the 9 nodes from each
face "facing" - perpendicular to - the x-axis).
I see that Hermite elements do not appear to be implemented. In
answering a previous reply from Wolfgang:
>> I am looking at trying to implement the finite element solution of MHD
>> equations using dealii and would need to be able to use a hermite
element.
>Are these the elements that have values and gradients as degrees of
freedom in
>each vertex? Baerbel Janssen has implemented the Adini element that does
>something similar I believe.
>Do you plan on using this for a mesh with only rectangular cells, or
does it
>have general, unstructured meshes? The difficulty with all of these
elements
>that have derivatives as degrees of freedom is the transformation from
>reference to real cell since the xi_1 derivative may be the x_1
derivative on
>one cell that is a rectangle parallel to the coordinate axes, but may
be the
>derivative in an entirely different direction if the neighboring cell
is not a
>rectangle.
These elements have values and gradients at mid-edges and mid-faces
( for the x-direction on the reference cell [0,1]^{3}, the middle 9
nodes on the
the plane x = 1/2 taken from a 27 noder)
I believe I could do the modeling with pure rectangular cells (just
affine transformations
of the reference cell).
Thanks for all the help you guys. I hope someone can help with this.
Dan Brauss
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