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

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

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