We present commuting projection operators on de Rham sequences of two-dimensional multipatch spaces with local tensor-product parametrization and non-matching interfaces. Our construction yields projection operators which are local and stable in any $L^p$ norm with $p \in [1,\infty]$: it applies to shape-regular spline patches with different mappings and local refinements, under the assumption that neighboring patches have nested resolutions and that interior vertices are shared by exactly four patches. It also applies to de Rham sequences with homogeneous boundary conditions. Following a broken-FEEC approach, we first consider tensor-product commuting projections on the single-patch de Rham sequences, and modify the resulting patch-wise operators so as to enforce their conformity and commutation with the global derivatives, while preserving their projection and stability properties with constants independent of both the diameter and inner resolution of the patches.

翻译：我们提出了在二维多片空间de Rham序列上，具有局部张量积参数化和非匹配接口的交换投影算子。我们的构造生成了在任意$p \in [1,\infty]$的$L^p$范数下局部且稳定的投影算子：该构造适用于具有不同映射和局部细化的形状正则样条片，前提是相邻片具有嵌套分辨率且内部顶点恰好由四个片共享。该方法同样适用于带齐次边界条件的de Rham序列。遵循破碎-FEEC方法，我们首先考虑单片de Rham序列上的张量积交换投影，并修正所得的逐片算子，以强制其满足全局导数的共形性和交换性，同时保持其投影和稳定性性质，且常数独立于片的直径和内部分辨率。