An arbitrary-order discrete de Rham complex on polyhedral meshes. Part II: Consistency
Abstract
In this paper we prove a complete panel of consistency results for the discrete de Rham (DDR) complex introduced in the companion paper [D. A. Di Pietro and J. Droniou, An arbitrary-order discrete de Rham complex on polyhedral meshes. Part I: Exactness and Poincar\'e inequalities, 2021, submitted], including primal and adjoint consistency for the discrete vector calculus operators, and consistency of the corresponding potentials. The theoretical results are showcased by performing a full convergence analysis for a DDR approximation of a magnetostatics model. Numerical results on three-dimensional polyhedral meshes complete the exposition.
Cite
@article{arxiv.2101.04946,
title = {An arbitrary-order discrete de Rham complex on polyhedral meshes. Part II: Consistency},
author = {Daniele Antonio Di Pietro and Jérôme Droniou},
journal= {arXiv preprint arXiv:2101.04946},
year = {2021}
}
Comments
This paper was merged with the previous "Part I", and both are now available as a single paper at arXiv:2101.04940