Tabulation of function space V

f_n = u *v is just a symbolic expression, no computation or modification of dof coordinates has happened yet.

When you call
dolfinx.fem.form(f_n*ufl.dx) C++ code is generated for assembly of the local element tensor.

Calling assemble_matrix on this object assembles the contributions into a global tensor.

If you want to control the integration points, you can set “quadrature_degree” in ufl.Measure, see for instance:

To inspect these coordinates you should look at Crash when trying to obtain coordinates of quadrature points - #2 by dokken
Mapped quadrature points, weights and solution at these quadrature points - #2 by dokken

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