Journal of Scientific Computing

, Volume 72, Issue 3, pp 1196–1213 | Cite as

Relaxing the CFL Condition for the Wave Equation on Adaptive Meshes

  • Daniel Peterseim
  • Mira Schedensack


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.


CFL condition Hyperbolic equation Finite element method Adaptive mesh refinement 

Mathematics Subject Classification

65M12 65M60 35L05 



The authors would like to thank Andreas Longva for pointing out that mass lumping indeed works. Parts of this paper were written while the authors enjoyed the kind hospitality of the Hausdorff Institute for Mathematics (Bonn).


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Institut für Numerische SimulationUniversität BonnBonnGermany

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