Abstract
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
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