non-conforming hexehedral meshes

[adorate...@gmail.com]

Hi

I am a PhD student and I intend to use dealii for geomechanic simulations (probably in poroelasticity). One of my colleague works on mesh generation of geological model. He noticed that deal.ii use non-conforming mesh after the refine step. Apparently, this type of mesh is hard to tackle in a fem code and can lead to an inaccurate result.

https://hal.archives-ouvertes.fr/hal-01313285/document

I don’t know if people are concerned about this. Even commercial code didn’t handle this. Does deal.ii take this into account?

Cheers

Nicolas

[Wolfgang Bangerth]

Nicolas,
there are plenty of commercial codes that use hanging nodes in the same way as
deal.II does. It is true that it's difficult to *implement*, but I have not
heard any *theoretical* reason why hanging nodes shouldn't be used.

I only spent a few minutes on the paper, but it does seem to suggest that
these "non-conforming" meshes work just fine -- all of the graphs show the
correct convergence order. Can you point out where they talk about the
"inaccurate result"?

Best
W.

--
------------------------------------------------------------------------
Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[adorate...@gmail.com]

Hi

Thanks for your response.
If deal.II handles hanging nodes in the same way as other codes that's fine for me. I will recommend my colleague to study your lecture 16. I think it explains how to deal with this kind of mesh.
I think they have trouble with the discontinuity of the shape functions (or other finite element functions) but you explain in your lecture how to add constraints to ensure continuity.
I guess the need for refined meshes lead you to make this second version of deal.

PS: Thanks for your MATH 676 lectures, they are so helpful for my PhD.

Best regards

Nicolas

[Wolfgang Bangerth]

Nicolas,

> If deal.II handles hanging nodes in the same way as other codes that's fine
> for me.

Yes, there is really only one canonical way for dealing with hanging nodes
that everyone uses (including deal.II).

> I will recommend my colleague to study your lecture 16. I think it
> explains how to deal with this kind of mesh. I think they have trouble with
> the discontinuity of the shape functions (or other finite element
> functions) but you explain in your lecture how to add constraints to ensure
> continuity. I guess the need for refined meshes lead you to make this
> second version of deal.

Actually, the original DEAL library did that as well. It was more a question
of software design that prompted us to rewrite it all.

> PS: Thanks for your MATH 676 lectures, they are so helpful for my PhD.

Thank you for the kind words!

Best
Wolfgang