Relaxing the CFL condition for the wave equation on adaptive meshes
Relaxing the CFL condition for the wave equation on adaptive meshes
Dokument öffnen (669.3KB)Datum der Veröffentlichung
02.2017Verlag / herausgebende Einrichtung
Institut für Numerische Simulation (INS)Verlagsort
BonnMetadaten
Zur Langanzeige
Zitierbarer Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11859
Inhalt
The Courant-Friedrichs-Lewy (CFL) condition guarantees the stability of the popular explicit leapfrog method for the wave equation. However, it limits the choice of the time step size to be bounded by the minimal mesh size in the spatial finite element mesh. This essentially prohibits any sort of adaptive mesh refinement that would be required to reveal optimal convergence rates on domains with re-entrant corners. This paper shows how a simple subspace projection step inspired by numerical homogenisation can remove the critical time step restriction so that the CFL condition and approximation properties are balanced in an optimal way, even in the presence of spatial singularities.
Schlagwörter
CFL condition, hyperbolic equation, finite element method, adaptive mesh refinement
Klassifikation (DDC)
510 Mathematik 518 Numerische AnalysisErstpublikation
https://ins.uni-bonn.de/publication/preprintsZugehörige Publikation(en)
https://doi.org/10.1007/s10915-017-0394-yReihe, Nummer
INS Preprints ; 1602Peterseim, Daniel; Schedensack, Mira: Relaxing the CFL condition for the wave equation on adaptive meshes. In: INS Preprints, 1602.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11859
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11859
@unpublished{handle:20.500.11811/11859,
author = {{Daniel Peterseim} and {Mira Schedensack}},
title = {Relaxing the CFL condition for the wave equation on adaptive meshes},
publisher = {Institut für Numerische Simulation (INS)},
year = 2017,
month = feb,
INS Preprints},
volume = 1602,
note = {The Courant-Friedrichs-Lewy (CFL) condition guarantees the stability of the popular explicit leapfrog method for the wave equation. However, it limits the choice of the time step size to be bounded by the minimal mesh size in the spatial finite element mesh. This essentially prohibits any sort of adaptive mesh refinement that would be required to reveal optimal convergence rates on domains with re-entrant corners. This paper shows how a simple subspace projection step inspired by numerical homogenisation can remove the critical time step restriction so that the CFL condition and approximation properties are balanced in an optimal way, even in the presence of spatial singularities.},
url = {https://hdl.handle.net/20.500.11811/11859}
}
author = {{Daniel Peterseim} and {Mira Schedensack}},
title = {Relaxing the CFL condition for the wave equation on adaptive meshes},
publisher = {Institut für Numerische Simulation (INS)},
year = 2017,
month = feb,
INS Preprints},
volume = 1602,
note = {The Courant-Friedrichs-Lewy (CFL) condition guarantees the stability of the popular explicit leapfrog method for the wave equation. However, it limits the choice of the time step size to be bounded by the minimal mesh size in the spatial finite element mesh. This essentially prohibits any sort of adaptive mesh refinement that would be required to reveal optimal convergence rates on domains with re-entrant corners. This paper shows how a simple subspace projection step inspired by numerical homogenisation can remove the critical time step restriction so that the CFL condition and approximation properties are balanced in an optimal way, even in the presence of spatial singularities.},
url = {https://hdl.handle.net/20.500.11811/11859}
}
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