chapter
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P

XT = {κ : VT → C, κ(u) = φ(F)u), φ ∈ Xk}.

Sloppily speaking, this means that both the geometric elements and the local spaces can be mapped onto each other, and that the local degrees of freedom are invariant with respect

to pull-back. An important consequence is that nodal interpolation operators and pull-backs commute:

F)(Ihu|T ) = Ih(F)(u))|K, for all sufficient smooth functions/vector fields u on T .