𝐿¹-error estimates for numerical approximations of Hamilton-Jacobi-Bellman equations in dimension 1

Bokanowski, Olivier; Forcadel, Nicolas; Zidani, Hasnaa

doi:10.1090/S0025-5718-10-02311-2

$L^1$-error estimates for numerical approximations of Hamilton-Jacobi-Bellman equations in dimension 1
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by Olivier Bokanowski, Nicolas Forcadel and Hasnaa Zidani PDF

Math. Comp. 79 (2010), 1395-1426 Request permission

Abstract:

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 $L^1$-error estimates for both schemes. We also provide numerical examples to validate their accuracy in solving smooth and discontinuous solutions.

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