Convergence of an Antidiffusion Lagrange-Euler Scheme for Quasilinear Equations

This paper presents an explicit scheme which may be broken into several steps. The first one is a transport phase for a time step, with a projection on a Lagrangian mesh. Then a new projection is performed on a fixed Eulerian mesh. Lastly a corrected antidiffusion step of the SHASTA type occurs. A s...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 1984-10, Vol.21 (5), p.985-994
Main Authors: Le Roux, A. Y., Quesseveur, P.
Format: Article
Language:English
Subjects:
Entropy
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Summary:This paper presents an explicit scheme which may be broken into several steps. The first one is a transport phase for a time step, with a projection on a Lagrangian mesh. Then a new projection is performed on a fixed Eulerian mesh. Lastly a corrected antidiffusion step of the SHASTA type occurs. A stability condition appears to make the scheme easily computable. This condition allows larger timesteps than the well known Courant-Friedrichs-Lewy condition. A more complex version of the scheme is proposed, which works without any stability condition. Convergence towards the entropy solution is proved. A few numerical experiments are reported, showing the quality of the approximation of shocks or giving some information about the precision.
ISSN:0036-1429
1095-7170
DOI:10.1137/0721061