Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Mathematical Models and Methods in Applied Sciences Year : 2020

Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra

Abstract

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 sequence of 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.
Fichier principal
Vignette du fichier
ddr.pdf (377.85 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-02356810 , version 1 (09-11-2019)
hal-02356810 , version 2 (04-06-2021)

Identifiers

Cite

Daniele Antonio Di Pietro, Jerome Droniou, Francesca Rapetti. Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra. Mathematical Models and Methods in Applied Sciences, 2020, 30 (9), pp.1809-1855. ⟨10.1142/S0218202520500372⟩. ⟨hal-02356810v2⟩
281 View
188 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More