Dear David,

Thank you very much for your answer.

To satisfy my curiosity, let me ask a question. I had the feeling, based of the Periodic table of the finite elements, that the name of the function space should be "S".

So I moved to the firedrake/src/firedrake directory and ran : grep -ri functionspace * | grep \"S

But I did not get any example of the "S" function space. Are there examples of the usage of such finite elements?

The reason of my question is that I run benchmarks between industrial finite element software and firedrake. Everything is OK with simplical finite elements but I get different results when using Serendipity elements.

I am wondering why and would like to investigate (integration schemes for instance?).

Best regards,

Nicolas

Le mar. 28 janv. 2020 à 10:32, Ham, David A <david.ham@imperial.ac.uk> a écrit :

Dear Nicolas,

The serendipity family is called “S” in Firedrake, so the following code would create a Serendipity 2 function space on a unit square:

In [1]: from firedrake import *

In [2]: mesh = UnitSquareMesh(10, 10, quadrilateral=True)

In [3]: fs = FunctionSpace(mesh, "S", 2)

You could also create a quad mesh in, for example, gmsh and read it in.

For the 3D case you would need to extrude a quad mesh, and the rest follows.

Regards,

DAvid

From: <firedrake-bounces@imperial.ac.uk> on behalf of Karin&NiKo <niko.karin@gmail.com>
Date: Friday, 24 January 2020 at 14:49
To: firedrake <firedrake@imperial.ac.uk>
Subject: [firedrake] Serendipity elements

Dear Firedrakers,

I would like to use continuous finite elements from the serendipity family. At the moment, I would like to use some simple quadratic 8-nodes quadrangles and 20-nodes hexaedra (the S2 element from the “Periodic table of the finite elements”).

I do not find any tests in Firedrake src (grep -ri functionspace * | grep \"S).

How can I do to use these finite elements?

Thanks,

Nicolas