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.

翻译：我们提出了在具有局部张量积参数化及非匹配界面的二维多块空间de Rham序列上的稳定交换投影算子。在相邻块具有嵌套分辨率且内部顶点恰好由四个块共享的假设下，我们的构造涵盖了具有不同映射的形状正则块与局部细化块的情况。遵循断裂-FEEC方法，我们首先在单块de Rham序列上应用张量积构造，并修改逐块交换投影算子以强制其符合性，同时保持算子原有的交换性、投影性与L2稳定性。所得算子具有局部性与L2稳定性，其常数独立于各独立块的大小和内部分辨率。