An anti-diffusive scheme for viability problems
Applied Numerical Mathematics - Numerical methods for viscosity solutions and applications
An Efficient Data Structure and Accurate Scheme to Solve Front Propagation Problems
Journal of Scientific Computing
A Discontinuous Galerkin Solver for Front Propagation
SIAM Journal on Scientific Computing
HJB approach for motion planning and reachabilty analysis
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
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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