Titre :

Damped energy-norm a posteriori error estimates using C2-reconstructions for the fully discrete wave equation with the leapfrog scheme

Auteur(s) :

Chaumont-Frelet, Théophile [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]
Ern, Alexandre [Auteur]
Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique [CERMICS]
Simulation for the Environment: Reliable and Efficient Numerical Algorithms [SERENA]

Date de publication :

2024-03-19

Mot(s)-clé(s) en anglais :

Leapfrog scheme
Time-integration
Wave equation
A posteriori error estimates
Finite element method

Discipline(s) HAL :

Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]

Résumé en anglais : [en]

We derive a posteriori error estimates for the the scalar wave equation discretized in space by continuous finite elements and in time by the explicit leapfrog scheme. Our analysis combines the idea of invoking extra ...
Lire la suite >We derive a posteriori error estimates for the the scalar wave equation discretized in space by continuous finite elements and in time by the explicit leapfrog scheme. Our analysis combines the idea of invoking extra time-regularity for the right-hand side, as previously introduced in the space semi-discrete setting, with a novel, piecewise quartic, globally twice-differentiable time-reconstruction of the fully discrete solution. Our main results show that the proposed estimator is reliable and efficient in a damped energy norm. These properties are illustrated in a series of numerical examples.Lire moins >

Langue :

Anglais

Projet ANR :

Estimation d'erreur a posteriori pour les équations d'ondes

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL