# How many integration points are included in the tetrahedral grid?

**URL:** <https://fenicsproject.discourse.group/t/how-many-integration-points-are-included-in-the-tetrahedral-grid/6429>\
**Category:** mesh\
**Created:** [August 22, 2021, 10:00am UTC](https://fenicsproject.discourse.group/t/how-many-integration-points-are-included-in-the-tetrahedral-grid/6429 "2021-08-22T10:00:39Z")\
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**Author:** ![dokken](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/dokken/32/1560_2.png) [@dokken](https://fenicsproject.discourse.group/u/dokken)\
**Post date:** [August 22, 2021, 1:04pm UTC](https://fenicsproject.discourse.group/t/how-many-integration-points-are-included-in-the-tetrahedral-grid/6429/2 "2021-08-22T13:04:27Z")

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The number of quadrature (gauss) points is estimated by ufl when you specify your variational form.  
See for instance:

```python
from dolfin import *

from ufl.algorithms.compute_form_data import estimate_total_polynomial_degree

mesh = UnitCubeMesh(5, 5, 5)
Vs = FunctionSpace(mesh, "P", 2)
u, v = TrialFunction(Vs), TestFunction(Vs)
a_mass = inner(u, v)*dx
a_stiffness = inner(grad(u), grad(v))*dx
L = inner(Function(Vs), v) * dx

print(estimate_total_polynomial_degree(a_mass))
print(estimate_total_polynomial_degree(a_stiffness))
print(estimate_total_polynomial_degree(a_mass + a_stiffness))
print(estimate_total_polynomial_degree(L))

```

You can specify the quadrature degree in the integration measure, i.e.:

```python
a_fixed_degree = inner(u, v)*dx(metadata={"quadrature_degree":2})

```

The schemes for the different degrees can be found at:

> <https://github.com/FEniCS/fiat/blob/master/FIAT/quadrature_schemes.py#L406-L519>

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