Anti-dissipative schemes for advection and application to Hamilton-Jacobi-Bellmann equations

Olivier Bokanowski (1, 2) , Hasnaa Zidani (1, 2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 OC - Optimisation et commande

We propose two new antidiffusive schemes for advection (or linear transport), one of them being a mixture of Roe's Super-Bee scheme and of the "Ultra-Bee" scheme. We show how to apply these schemes to treat time-dependent first order Hamilton-Jacobi-Bellman equations with discontinuous initial data, possibly infinitely-valued. Numerical tests are proposed, in one and two space dimensions, in order to validate the methods.

Domaines: Analyse numérique [math.NA]; Autre [cs.OH]

Olivier Bokanowski, Hasnaa Zidani. Anti-dissipative schemes for advection and application to Hamilton-Jacobi-Bellmann equations. Journal of Scientific Computing, 2007, 30 (1), pp.1-33. ⟨10.1007/s10915-005-9017-0⟩. ⟨hal-00878221⟩