We construct smooth finite elements spaces on Powell–Sabin triangulations that form an exact sequence. The first space of the sequence coincides with the classical \(C^1\) Powell–Sabin space, while the others form stable and divergence-free yielding pairs for the Stokes problem. We develop degrees of freedom for these spaces that induce projections that commute with the differential operators.

中文翻译：

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鲍威尔-萨宾分裂的精确序列

我们在形成精确序列的Powell-Sabin三角剖分上构造光滑有限元空间。序列的第一个空间与经典\（C ^ 1 \） Powell-Sabin空间重合，而其他空间则形成了Stokes问题的稳定且无散度的屈服对。我们为这些空间开发了自由度，这些空间诱发了与微分算子通勤的投影。