An arbitrary-order discrete de Rham complex on polyhedral meshes. Part II: Consistency

Autor:	Di Pietro, Daniele Antonio, Droniou, Jérôme
Rok vydání:	2021
Předmět:	Mathematics - Numerical Analysis 65N30 65N99 78A30
Druh dokumentu:	Working Paper
Popis:	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. Comment: This paper was merged with the previous "Part I", and both are now available as a single paper at arXiv:2101.04940
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2101.04946 Zobrazit plný text záznamu View this record from Arxiv