Why does ufl.Mesh() only take vector elements?

mesh
,
1

I’m trying to understand some of the finer details of UFL, but the documentation doesn’t explain ufl.Mesh(). This tutorial goes over how to use ufl.Mesh() to make a symbolic representation of the domain, but doesn’t say why it needs to take a vector element.

The following code produces an error when trying to use ufl.Mesh() with a scalar element.

import ufl
import basix.ufl

el=basix.ufl.element('Lagrange', 'triangle', 1)
domain=ufl.Mesh(el)

For context, I’m running this code in a Python3 kernel in a Jupyter Notebook out of the dolfinx/lab:stable Docker container.

Also, when might one want to use ufl.Mesh() instead of the dolfinx.mesh library?

2

It needs a vector element to represent each of the coordinates (x,y,z).

This is explained in even more detail at
http://jsdokken.com/FEniCS-workshop/src/finite_element_method/advanced_elements.html
which also covers when to use uf.Mesh
http://jsdokken.com/FEniCS-workshop/src/unified_form_language/ufl_elements.html#the-domain-omega
http://jsdokken.com/FEniCS-workshop/src/form_compilation/compile_form.html
http://jsdokken.com/FEniCS-workshop/src/form_compilation/alternate_form.html