In every finite element implementation, one works with degrees of freedom, i.e. unknown coefficients that one would like to solve an equation for,
Some notes about this can be found at:
https://scientificcomputing.github.io/mpi-tutorial/notebooks/dolfinx_MPI_tutorial.html#dolfinx-functions
See: How to get vertex values in dolfinx? - #17 by nav
which recommends interpolating into a first order Lagrange space (as that is what was done under the hood in compute_vertex_values, as shown in
Mapping of results to mesh nodes, debugging of dolfinx implentation of shell formulation - #6 by dokken
for facets:
Extract the coordinates of the boundary points and the value of a function on them - #4 by dokken