The discontinuous Galerkin approximation of the grad-div and curl-curl operators in first-order form is involution-preserving and spectrally correct - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Numerical Analysis Année : 2023

The discontinuous Galerkin approximation of the grad-div and curl-curl operators in first-order form is involution-preserving and spectrally correct

Résumé

The discontinuous Galerkin approximation of the grad-div and curl-curl problems formulated in conservative first-order form is investigated. It is shown that the approximation is spectrally correct, thereby confirming numerical observations made by various authors in the literature. This result hinges on the existence of discrete involutions which are formulated as discrete orthogonality properties. The involutions are crucial to establish discrete versions of weak Poincaré-Steklov inequalities that hold at the continuous level.
Fichier principal
Vignette du fichier
spectrum.pdf (610.25 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04003475 , version 1 (24-02-2023)
hal-04003475 , version 2 (29-06-2023)

Identifiants

Citer

Alexandre Ern, Jean-Luc Guermond. The discontinuous Galerkin approximation of the grad-div and curl-curl operators in first-order form is involution-preserving and spectrally correct. SIAM Journal on Numerical Analysis, 2023, 61 (6), pp.2940-2966. ⟨10.1137/23M1555235⟩. ⟨hal-04003475v2⟩
143 Consultations
146 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More