In this work, merging ideas from compatible discretisations and polyhedral methods, we construct novel fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra. The spaces and operators that appear in these sequences are directly amenable to computer implementation. Besides proving the exactness, we show that the usual three-dimensional sequence of trimmed Finite Element (FE) spaces forms, through appropriate interpolation operators, a commutative diagram with our sequence, which ensures suitable approximation properties. A discussion on reconstructions of potentials and discrete [Formula: see text]-products completes the exposition.

中文翻译：

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多边形和多面体上任意次数的完全离散多项式 de Rham 序列

在这项工作中，融合了兼容离散化和多面体方法的思想，我们在多边形和多面体上构建了具有任意度数的新型完全离散多项式 de Rham 序列。出现在这些序列中的空格和运算符可以直接通过计算机实现。除了证明准确性之外，我们还展示了通常的修剪有限元 (FE) 空间的三维序列通过适当的插值算子与我们的序列形成一个交换图，这确保了合适的近似属性。对势和离散[公式：见文本]-产品的重构的讨论完成了阐述。