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