Abstract: This paper is concerned with numerical approximation of viability kernels. We use a characterization of the viability kernel by the value function of an optimal control problem. Since this value function is discontinuous, usual discretization schemes (such as finite differences) provide poor approximation quality because of numerical diffusion. We investigate the use of the ultra-bee scheme for its anti-diffusive property in the transport of discontinuous functions. Numerical experiments, compared with the viability algorithm , show the relevance of this scheme for computing viability kernels and capture basins on several benchmark problems.