Anti-dissipative methods for Hamilton Jacobi Bellman equations.

Summary We study the convergence of an anti-dissipative scheme, the UltraBee, for Hamilton Jacobi Bellman equations in dimension 1. Two solution methods using this scheme are proposed. The first one combines the UltraBee with a grid adaptation, the second one uses a hollow storage. The latter is applied to the problem of atmospheric reentry. Finally, some theoretical extensions are given.