Mardal-Tai-Winther finite element

Question

Hi,
I'm using dolfin (C++) and I would like to use MTW finite elements.
In the manual they are referred as partially supported and in fact when I compile with ffc I get the following error:

*** FFC: Sorry, finite element of type "Mardal-Tai-Winther" are not supported by FIAT.

Is there any way in which I can use them? Maybe they have been implemented in the development version? Or maybe they are available with python interface?

Thanks a lot

Marco

Answer 1

MTW elements are not supported. We did some preliminary work several years ago representing them in FIAT, but they require a special-purpose transformation from the reference element (not Piola or affine mapping) to preserve the degrees of freedom. This transformation has not been put into the code generation process, so they are not accessible from C++ or Python either.

The same applies for Argyris and Hermite elements, too.

Comments

Thanks. Do you know if they are "available" in some other ways ? Because I've seen that prof. Mardal is also one of the author of the Fenics books/ developers, and so I was wondering if someone else had previously tried to implement them.
Thanks again
Marco

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They may have done a diffpack or other implementation -- I'd check their papers and/or email the authors to see what they used for numerical results.

It would be a big undertaking, but it would be great if somebody jumped in to figure out how to plug nonstandard transformations into the toolchain.

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Thank you for your interest in this element!
We implemented it in Diffpack, which I don't have access to anymore.
I could however give you the exact expressions for the basis functions.

That said, I would be interested in bringing this element back into FEniCS. I
miss using it :) In particular because it has very nice stability properties...