L^1-error estimate for numerical approximations of Hamilton-Jacobi-Bellman equations in dimension 1. - Archive ouverte HAL Access content directly
Journal Articles Mathematics of Computation Year : 2010

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

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Olivier Bokanowski
Hasnaa Zidani

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#### 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.

### Dates and versions

inria-00267644 , version 1 (28-03-2008)

### Identifiers

• HAL Id : inria-00267644 , version 1

### Cite

Olivier Bokanowski, Nicolas Forcadel, Hasnaa Zidani. L^1-error estimate for numerical approximations of Hamilton-Jacobi-Bellman equations in dimension 1.. Mathematics of Computation, 2010, 79 (271), pp.1395--1426. ⟨inria-00267644⟩

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