Broken-FEEC approximations of Hodge Laplace problems

In this article we study nonconforming discretizations of Hilbert complexes that involve broken spaces and projection operators to structure-preserving conforming discretizations. Under the usual assumptions for the underlying conforming subcomplexes, as well as stability and moment-preserving properties for the conforming projection operators, we establish the convergence of the resulting nonconforming discretizations of Hodge-Laplace source and eigenvalue problems.