How to get quadrature points and their weights?

1

In the previous FEniCS version, quadrature points and corresponding weights can be calculated like this:

from ffc.quadrature_schemes import create_quadrature

shape = "tetrahedron"
degree = 2
scheme="default"

(points, weights) = create_quadrature(shape, degree, scheme)

Is there any similar function in the current version of FEniCS?

2

Hi,
Looking at the repo, this seems to be what you are looking for:

from ffc.fiatinterface import create_quadrature as cquad
shape = "triangle"
deg = 2
scheme = "default"

points, weights = cquad(shape, deg, scheme)
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3

Thank you. This is what I was looking for.

4

Can we know the shape functions used for tetrahedron and default scheme in FEniCS?

Any help is appreciated.

5

Are you using legacy DOLFIN or DOLFINx?

The general shape functions used for Lagrangian elements order 1: https://defelement.com/elements/examples/tetrahedron-Lagrange-1.html, order 2: https://defelement.com/elements/examples/tetrahedron-Lagrange-2.html is listed in the links provided.

The default quadrature scheme is shown in:

and you can read the docs describing what rules it uses at:

and the rules for tetrahedra are shown here:

In general, you can use Symfem:GitHub - mscroggs/symfem: A symbolic finite element definition library to get the symbolic representation of a basis function.

python3 -m pip install symfem

order = 1
print(symfem.create_element("tetrahedron", "Lagrange", order).get_basis_functions())

returning:

[-x - y - z + 1, x, y, z]
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6

Hello, Can we print the Jacobian data?

from dolfin import *
from ufl import Jacobian
mesh= UnitSquareMesh(1,1)
t = Jacobian(mesh)

How can I excess the Jacobian matrix from t for each element?

7

You cannot get that in legacy DOLFIN without doing a projection of each component into a tensor space of DG-0 elements.

In DOLFINx this is easily available by using dolfinx.fem.Expression

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