Dear Nicolas,

You are very correct. Serendipity elements can defeat the quadrature degree estimator, resulting in inadvertent underintegration. Embarrassingly, we seem to have forgotten to merge the branch with the tests on it. These tests do manually set the quadrature degree. You can find them at: https://github.com/firedrakeproject/firedrake/pull/1430/files I will update that PR and merge it assuming it still passes.

Regards,

David

From: Karin&NiKo <niko.karin@gmail.com>
Date: Tuesday, 28 January 2020 at 12:19
To: David Ham <david.ham@imperial.ac.uk>
Cc: firedrake <firedrake@imperial.ac.uk>
Subject: Re: [firedrake] Serendipity elements

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