||In the present work, we show that the Lagrange–projection scheme
presented in Coquel et al.’s paper (Math. of Comp. 79.271 (2010): 1493–
1533), is asymptotic preserving for isentropic Euler equations, i.e. at the dis-
crete level it preserves the incompressible limit, satisfies the div-free condition
as well as the asymptotic expansion for the density in the continuous level.
Moreover, we prove that the scheme is positivity-preserving, L∞ -stable and entropy-admissible under some Mach-uniform restrictions. The analysis is similar to what has been presented in the original paper, but with the emphasis on the uniformity regarding the Mach number.