Rannacher-Turek Element Implementation

[sblauth]

Hi,

I have opened this issue to ask, whether there are any plans to implement the Rannacher-Turek element https://defelement.org/elements/rannacher-turek.html for quad and hex cells. Both in legacy FEniCS and FEniCSx, the Crouzeix-Raviart element (the analogon for triangles and tets https://defelement.org/elements/crouzeix-raviart.html) is implemented - so I thought that this would be a nice addition for FEniCSx, as it can handle quads and hex cells.

As there are parametric and non-parametric versions of these elements https://doi.org/10.1002/num.1690080202, with the non-parametric ones being more robust for anisotropic meshes, I would like to ask

• which version of the elements are implemented in basix (for the CR element)? I guess it is the parametric one
• would it be possible to also implement a non-parametric version?

Thanks a lot!

[mscroggs]

Hello,

Adding the Rannacher-Turek element isn't hard, I can do that this week. Related issue: #429

FEniCS supports the parametric versions of these elements, as there's currently hard assumptions that every element is defined on a reference cell the pushed forward. Implementing non-parametric elements like this is not impossible, but needs a significant amount of work so in the short term it won't be possible to do this.