Damped energy-norm a posteriori error estimates for fully discrete approximations of the wave equation using C2-reconstructions - Inria - Institut national de recherche en sciences et technologies du numérique
Preprints, Working Papers, ... Year : 2024

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

Abstract

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.
Fichier principal
Vignette du fichier
chaumontfrelet_ern_2024a.pdf (834.73 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04511867 , version 1 (19-03-2024)

Licence

Identifiers

Cite

Théophile Chaumont-Frelet, Alexandre Ern. Damped energy-norm a posteriori error estimates for fully discrete approximations of the wave equation using C2-reconstructions. 2024. ⟨hal-04511867⟩
40 View
23 Download

Altmetric

Share

More