[deal.II] Locally divergence free DG basis

[Florian Schulze]

Dear all,


i.e. an FE basis 𝛟(𝐱) that fulfils ∇⋅𝛟(𝐱) = 0 on the cell.



I found that this topic was already discussed in the forum before:

 * Locally divergence free FE space
   <https://groups.google.com/g/dealii/c/uGY2ltkMJ-E/m/6KzZm1u6l-EJ>
 * Custom shapeset questions
   <https://groups.google.com/g/dealii/c/NDiUu3qESOM/m/magIbF_FCQAJ>

But I don’t see that it made it into deal.II.
Am I missing something? Does deal.II have a divergence free FE basis?
Or does someone already have/know of an implementation?

If not, what would be the best way to go about implementing it?

I am trying to solve the magnetohydrodynamics (MHD) equations using the discontinuous Galerkin method with deal.II. Currently, I face the problem of the divergence free condition of the magnetic field, ∇⋅𝐁 = 0. One of the ways I want to address this problem is using locally divergence free elements, (Face jumps of the normal component can still introduce divergence globally - I plan to use different methods to deal with that.) After a short look in the documentation, seems like implementing a new TensorPolynomial <https://www.dealii.org/current/doxygen/deal.II/classTensorPolynomialsBase.html> and using with in the FE_DGVector <https://www.dealii.org/current/doxygen/deal.II/classFE__DGVector.html> is a possibility?

Thanks for your help!

Best,
Florian Schulze

​

--
The deal.II project is located at http://www.dealii.org/
For mailing list/forum options, see 
https://groups.google.com/d/forum/dealii?hl=en

To unsubscribe from this group and stop receiving emails from it, send an email 
to dealii+unsubscr...@googlegroups.com.
To view this discussion visit 
https://groups.google.com/d/msgid/dealii/5c8471a0-fec5-48cb-b531-185596e678f9%40mpi-hd.mpg.de.

--- You received this message because you are subscribed to the Google Groups "deal.II User Group" group.

smime.p7s
Description: S/MIME Cryptographic Signature