Journal of Computational Physics
Adaptive spline interpolation for Hamilton-Jacobi-Bellman equations
Applied Numerical Mathematics - Numerical methods for viscosity solutions and applications
Stochastic skiba sets: an example from models of illicit drug consumption
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
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Generalizing an idea from deterministic optimal control, we construct a posteriori error estimates for the spatial discretization error of the stochastic dynamic programming method based on a discrete Hamilton–Jacobi–Bellman equation. These error estimates are shown to be efficient and reliable, furthermore, a priori bounds on the estimates depending on the regularity of the approximate solution are derived. Based on these error estimates we propose an adaptive space discretization scheme whose performance is illustrated by two numerical examples.