Gauss-compatible Galerkin schemes for time-dependent Maxwell equations

Abstract : In this article we propose a unified analysis for conforming and non-conforming finite element methods that provides a partial answer to the problem of preserving discrete divergence constraints when computing numerical solutions to the time-dependent Maxwell system. In particular, we formulate a compatibility condition relative to the preservation of genuinely oscillating modes that takes the form of a generalized commuting diagram, and we show that compatible schemes satisfy convergence estimates leading to long-time stability with respect to stationary solutions. These findings are applied by specifying compatible formulations for several classes of Galerkin methods, such as the usual curl-conforming finite elements and the centered discontinuous Galerkin (DG) scheme. We also propose a new conforming/nonconforming Galerkin (Conga) method where fully discontinuous solutions are computed by embedding the general structure of curl-conforming finite elements into larger DG spaces. In addition to naturally preserving one of the Gauss laws in a strong sense, the Conga method is both spectrally correct and energy conserving, unlike existing DG discretizations where the introduction of a dissipative penalty term is needed to avoid the presence of spurious modes.
Type de document :
Article dans une revue
Mathematics of Computation, American Mathematical Society, 2016, 85
Liste complète des métadonnées

Littérature citée [36 références]  Voir  Masquer  Télécharger
Contributeur : Martin Campos Pinto <>
Soumis le : mercredi 24 juin 2015 - 12:48:29
Dernière modification le : vendredi 4 janvier 2019 - 17:32:31
Document(s) archivé(s) le : mardi 25 avril 2017 - 18:17:15


Fichiers produits par l'(les) auteur(s)


  • HAL Id : hal-00969326, version 2


Martin Campos Pinto, Eric Sonnendrücker. Gauss-compatible Galerkin schemes for time-dependent Maxwell equations. Mathematics of Computation, American Mathematical Society, 2016, 85. 〈hal-00969326v2〉



Consultations de la notice


Téléchargements de fichiers