Title :

Damped energy-norm a posteriori error estimates for fully discrete approximations of the wave equation using C2-reconstructions

Author(s) :

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

Publication date :

2024-03-19

English keyword(s) :

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

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

ANR Project :

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

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL