Damped energy-norm a posteriori error ...
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Title :
Damped energy-norm a posteriori error estimates using C2-reconstructions for the fully discrete wave equation with the leapfrog scheme
Author(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]
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]
Publication date :
2024-03-19
English keyword(s) :
Leapfrog scheme
Time-integration
Wave equation
A posteriori error estimates
Finite element method
Time-integration
Wave equation
A posteriori error estimates
Finite element method
HAL domain(s) :
Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
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 >
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
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Submission date :
2025-01-24T13:43:05Z
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