A characterization of Whitney forms

Abstract

We give a characterization of Whitney forms on an n n -simplex σ \sigma and prove that for every real valued simplicial k k -cochain c c on σ \sigma , the form W c Wc is the unique differential k k -form φ \varphi on σ \sigma with affine coefficients that pulls back to a constant form of degree k k on every k k -face τ \tau of σ \sigma , and satisfies ∫ τ φ => c , τ > \int _{\tau } \varphi = >c,\tau > .