second-order derivatives for vector finite elements

Main Forum Old-Forum - do not post here
1

Hello,

I am not sure how to get the second-order derivative information for the edge elements.
For H1 space, we can do v.Operator(“hesse”), but it seems that this operator is not implemented for vector finite elements yet… Do you have any suggestions?

Best,
Guosheng

2

Hi Guosheng,
Do you need it for postprocessing? You could project the function on a VectorH1 of higher order and then take the gradient. If you need it in the form, I think you would need to implement and export it.

Best
Christopher

3

Christopher,

I actually need it for the form. It’s a forth-order vector PDE.
I am a bit scared to dig into the c++ code myself. But maybe it worth a try.
As a first step, I just want to work on square/box elements, which might also makes the coding less intensive. Can you suggest where to start with?

Best,
Guosheng

4

Hi Guosheng,

have you tried a mixed formulation to reduce the fourth-order problem to two second-order problems like the Hellan-Herrmann-Johnson method in this tutorial?

Then you maybe could avoid the Hessian operator.

Best
Michael

5

Hello Michael,

I am following the demo: The Hellan-Herrmann-Johnson Mixed Method. I would like to know the explicit basis functions for the bending moments, could you point out some accessible references on this for an engineering background user. Many thanks!!

Sincerely,

Bin

6

Hi Bin,
have a look into the PhD thesis by Astrid Pechstein (aka Astrid Sinwel). Chapter 4.4, in particular page 79.
TDNNS and HHJ use the same finite element spaces for the stress (or moments).
available from here:
http://www.numa.uni-linz.ac.at/Teaching/PhD/Finished/sinwel-diss.pdf
best, Joachim

7

May thanks Joachim!!

8

Hi Guosheng,

Philip has now finished the paper on the mixed method using a stream-function,
similar to the HHJ method. It’s available on arXiv:

Joachim

9

Hi Joachim,

Thanks for the info. I also noticed that paper on arXiv.

Best,
Guosheng