What FEspace is HDivSurface

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1

Is it BDM or RT? When I set e.g. order=3, does that mean that the divergence space is SurfaceL2, order=2?

Best regards,

Alvar

2

Hi Alvar,

you can think of the HDivSurface as the 2D HDiv space mapped onto the surface.
With order=3 you get the BDM_3 space and thus the divergence should be in SurfaceL2 with order=2.

Best,
Michael

3

Hi Michael,

Thank you for your reply and the clarification. Just out of curiosity, as I understand it the construction of the FE-space would also be possible with Raviart-Thomas elements. Is there a way one could use these elements?

Best regards,

Alvar

4

Hi Alvar,

using

fes = HDiv(mesh, order=k, RT=True)

gives the Raviart-Thomas elements (for triangles and tetrahedra), which lie between polynomials of order k and k+1 and the divergence is then in L2 of order k.

For HDivSurface this option is currently not implemented in the main code, but it might come soon.

Best,
Michael

5

The Raviart-Thomas elements should now be available for the HDivSurface space for the latest nightly build version.