Finite Volume Transport Schemes

Bruno Després (1)

1 LJLL - Laboratoire Jacques-Louis Lions

We analyze arbitrary order linear nite volume transport schemes and show asymptotic stability in L1 and L1 for odd order schemes in dimen- sion one. It gives sharp fractional order estimates of convergence for BV solutions. It shows odd order nite volume advection schemes are better than even order nite volume schemes. Therefore the Gibbs phenomena is controled for odd order nite volume schemes. Numerical experiments sustain the theoretical analysis. In particular the oscillations of the Lax- Wendro scheme for small Courant numbers are correlated with its non stability in L1. A scheme of order three is proved to be stable in L1 and L1.

Domaines: Analyse numérique [math.NA]

Bruno Després. Finite Volume Transport Schemes. 2006. ⟨hal-00121923⟩