CONVERGENCE OF AN ANTIDIFFUSION LAGRANGE-EULER SCHEME FOR QUASI-LINEAR EQUATIONS

The authors present 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.