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 exactness, we show that the usual three-dimensional sequence of trimmed Finite Element 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 $L^2$-products completes the exposition.
翻译:在这项工作中,将兼容的离散和多面方法的理念结合起来,我们在多边形和多面形上构建了全新的完全独立的任意度多面形Rham序列。在这些序列中出现的空间和操作器直接可直接用于计算机实施。除了证明准确性外,我们展示出通常的三维三维三维三维三维三边形的三边形三边形,通过适当的内插操作器,一个与我们序列的通融图,确保适当的近似特性。关于重建潜力和离散的$L$2美元产品的讨论完成了这一解释。