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L^1-error estimate for numerical approximations of Hamilton-Jacobi-Bellman equations in dimension 1

Bokanowski, Olivier; Forcadel, Nicolas; Zidani, Hasnaa (2010), L^1-error estimate for numerical approximations of Hamilton-Jacobi-Bellman equations in dimension 1, Mathematics of Computation, 79, 271, p. 1395-1426. http://dx.doi.org/10.1090/S0025-5718-10-02311-2

Type
Article accepté pour publication ou publié
External document link
http://hal.inria.fr/inria-00267644
Date
2010
Journal name
Mathematics of Computation
Volume
79
Number
271
Publisher
AMS
Pages
1395-1426
Publication identifier
Metadata
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Author(s)
Bokanowski, Olivier cc

Forcadel, Nicolas cc

Zidani, Hasnaa
Abstract (EN)
The goal of this paper is to study some numerical approximations of particular Hamilton-Jacobi-Bellman equations in dimension 1 and with possibly discontinuous initial data. We investigate two anti-diffusive numerical schemes; the first one is based on the Ultra-Bee scheme, and the second one is based on the Fast Marching Method. We prove the convergence and derive L1-error estimates for both schemes. We also provide numerical examples to validate their accuracy in solving smooth and discontinuous solutions.
Subjects / Keywords
HJB equation; Fast Marching Method; Ultr-Bee scheme; L1-error estimates; antidiffusive scheme