Anti-dissipative schemes for advection and application to Hamilton-Jacobi-Bellman equations
Résumé
We propose two new anti-diffusive schemes for advection (or linear transport), one of them being a mixture of Roe's SuperBee scheme and of the UltraBee scheme. We show how to apply these schemes to treat time-dependant 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.