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In this paper, a unified family, for any $n\geqslant 2$ and $1\leqslantk\leqslant n-1$, of nonconforming finite element schemes are presented for theprimal weak formulation of the $n$-dimensional Hodge-Laplace equation on$H\Lambda^k\cap H^*_0\Lambda^k$ and on the simplicial subdivisions of thedomain. The finite element scheme possesses an $\mathcal{O}(h)$-orderconvergence rate for sufficiently regular data, and an $\mathcal{O}(h^s)$-orderrate on any $s$-regular domain, $0<s\leqslant 1$, no matter what topology thedomain has.

A primal finite element scheme of the Hodge Laplace problem