Cohomology of the discrete de Rham complex on domains of general topology

Abstract

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.

References in corpus (2)

• Arbitrary-order pressure-robust DDR and VEM methods for the Stokes problem on polyhedral meshes
• An arbitrary-order method for magnetostatics on polyhedral meshes based on a discrete de Rham sequence

Cited by in corpus (2)

• De Rham compatible Deep Neural Network FEM
• Uniform Poincaré inequalities for the Discrete de Rham complex on general domains