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German
Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations
L. Grüne:
Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations
in:
Numerical Methods for Viscosity Solutions and Applications,
M. Falcone, Ch. Makridakis
(eds.)
World Scientific,
Singapore,
2001,
153 - 172
Smart-Link:
http://www.worldscientific.com/
Keywords: semi-Lagrangian discretization; evolutive Hamilton-Jacobi-Bellmanequations; optimal control; error estimates; iterative procedure; adaptive
grids
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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.