Bounded commuting projections for multipatch spaces with non-matching interfaces

We present stable commuting projection operators on de Rham sequences of two-dimensional multipatch spaces with local tensor-product parametrization and non-matching interfaces. Our construction covers the case of shape-regular patches with different mappings and locally refined patches, under the assumption that neighbouring patches have nested resolutions and that interior vertices are shared by exactly four patches. Following a broken-FEEC approach we first apply a tensor-product construction on the single-patch de Rham sequences and modify the resulting patch-wise commuting projections to enforce their conformity while preserving their commuting, projection, and L2 stability properties. The resulting operators are local and stable in L2, with constants independent of both the size and the inner resolution of the individual patches.