论文标题
一般拓扑结构域的离散DE RHAM复合物的共同体学
Cohomology of the discrete de Rham complex on domains of general topology
论文作者
论文摘要
在这项工作中，我们证明，对于$ \ mathbb {r}^3 $的一般多面体域，[di pietro和droniou的离散de rham复合物的共同体学空间是一个任意的de roniou，一个任意的de rham de rham complex complect on Polyhedral complect on Polyhedral complect on Polyhectne Meshes：精确性，POINCREN，POINCARé不平等和一致性，找到。计算。 Math。，2021，doi：10.1007/s10208-021-09542-8]与连续De Rham复合物的同构是同构。据我们所知，这是由一般多面体网格构建的任意订购复合物的第一个结果。
In this work we prove that, for a general polyhedral domain of $\mathbb{R}^3$, the cohomology spaces of the discrete de Rham complex of [Di Pietro and Droniou, An arbitrary-order discrete de Rham complex on polyhedral meshes: Exactness, Poincaré inequalities, and consistency, Found. Comput. Math., 2021, DOI: 10.1007/s10208-021-09542-8] are isomorphic to those of the continuous de Rham complex. This is, to the best of our knowledge, the first result of this kind for an arbitrary-order complex built from a general polyhedral mesh.
