Frequency-explicit a posteriori error estimates for discontinuous Galerkin discretizations of Maxwell's equations - INRIA Chile Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Numerical Analysis Année : 2024

Frequency-explicit a posteriori error estimates for discontinuous Galerkin discretizations of Maxwell's equations

Résumé

We propose a new residual-based a posteriori error estimator for discontinuous Galerkin discretizations of time-harmonic Maxwell's equations in first-order form. We establish that the estimator is reliable and efficient, and the dependency of the reliability and efficiency constants on the frequency is analyzed and discussed. The proposed estimates generalize similar results previously obtained for the Helmholtz equation and conforming finite element discretization of Maxwell's equations. In addition, for the discontinuous Galerkin scheme considered here, we also show that the proposed estimator is asymptotically constantfree for smooth solutions. We also present two-dimensional numerical examples that highlight our key theoretical findings and suggest that the proposed estimator is suited to drive h and hp-adaptive iterative refinements.
Fichier principal
Vignette du fichier
chaumontfrelet_vega_2022a.pdf (25.11 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03744230 , version 1 (02-08-2022)

Licence

Identifiants

Citer

Théophile Chaumont-Frelet, Patrick Vega. Frequency-explicit a posteriori error estimates for discontinuous Galerkin discretizations of Maxwell's equations. SIAM Journal on Numerical Analysis, 2024, 62 (1), pp.400-421. ⟨10.1137/22M1516348⟩. ⟨hal-03744230⟩
76 Consultations
19 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More