Basis function ordering using T_apply

[dokken]

@Legat

When manually assembling any matrix, it is necessary to know which basis value computed in some point (quadrature for example, but not necessary) corresponds to which cell dof. From documentation it looks like function T_apply (dolfinx.fem — DOLFINx 0.10.0.0 documentation) should do what I’m looking for and rearrange basis functions values to match dof ordering.

T_apply is a dof transformation applied to elements which require them, see section 8.4 of: DOLFINx: The next generation FEniCS problem solving environment

Lagrange elements are not such an element, as the dofmap is permitted at the creation of the function space to account for a consistent ordering.

What you seem like you would like is the element-dof-layout: dolfinx.cpp.fem — DOLFINx 0.10.0.0 documentation
which tells you how each dof in V.cell_dofs(i) relates to the element entities. You can either look at the closure (for instance all dofs related to a facet, the edges of a facet and the vertices), or just those associated with such an entity.

See for instance: Moving submesh diverges from its designated trajectory in a two-phase problem - #2 by dokken for a use-case of finding the dofs associated with a given set of vertices.