Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations

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Grüne, Lars:
Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations.
In: Falcone, Maurizio ; Makridakis, Charalampos (Hrsg.): Numerical Methods for Viscosity Solutions and Applications. - Singapore : World Scientific , 2001 . - S. 153-172 . - (Series on Advances in Mathematics for Applied Sciences ; 59 )
ISBN 981-02-4717-6

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Abstract

We present an adaptive grid generation for a class of evolutive Hamilton-Jacobi-Bellman equations. Using a two step (semi-Lagrangian) discretization of the underlying optimal control problem we define a-posteriori local error estimates for the discretization error in space. Based on these estimates we present an iterative procedure for the generation of adaptive grids and discuss implementational details for a suitable hierarchical data structure.