Local finite element approximation of Sobolev differential forms

We address fundamental aspects in the approximation theory of vector-valued finite element methods, using exterior calculus as a unifying framework. generalize Clément interpolant and Scott-Zhang to differential forms, we derive broken Bramble-Hilbert lemma. Our interpolants require only minimal smoothness assumptions respect partial boundary conditions. This permits us state local error estimates terms mesh size. theoretical results apply curl-conforming divergence-conforming methods over simplicial triangulations.