2
$\begingroup$

For whatever reason, I stubbornly decided to use tetrahedral elements and find myself needing to use P3 elements with bubble functions ("P3b3d" in FREEFEM-style denomination).

The 2d case is fairly well documented, see e.g. here, and everyone is using it (P2b and P3b in FREEFEM).

The 3d case is more gnarly. There's a book by Cohen that explains some of the problems, and this paper claims to have some such elements.

A wrinkle in the thing is that the FREEFEM documentation claims that, for the P2b3d space, FREEFEM claims that it uses P2 plus a single bubble function $\lambda_1\lambda_2\lambda_3\lambda_4$, whereas Cohen's book also has "face bubbles". The P3b3d is not in Cohen's book, but it is in the paper I linked above.

Is there a modern book with these tetrahedral finite elements with bubble functions in it? Ideally in some detail? It's also called "lumped mass" or "stabilized". I don't care about the "stabilization" bit, I'm not doing wave equations.

I need these things because I need a lumped mass matrix that is positive definite.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
3
$\begingroup$

The lumped elements recently underwent some improvements, which are explained in detail in the following thesis

Sjoerd Geevers, Finite element methods for seismic modelling (English), University of Twente Doctoral Theses, Enschede: University of Twente (2018), ISBN 978-90-365-4613-3.

Improve this answer
$\endgroup$
2
  • $\begingroup$ Thanks, I'll take a look! $\endgroup$
    – Sébastien Loisel
    Commented Sep 19 at 21:48
  • $\begingroup$ That thesis is very clear, I'll take it! $\endgroup$
    – Sébastien Loisel
    Commented Sep 19 at 22:07

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .