Pré-Publication, Document De Travail Année : 2017

Error bounds for monotone schemes for parabolic Hamilton-Jacobi-Bellman equations in bounded domains

Résumé

We provide the rate of convergence of general monotone schemes for parabolic Hamilton-Jacobi-Bellman equations in bounded domains with strong Dirichlet boundary conditions. We work under the assumption of the existence of a sufficiently regular barrier function for the problem in order to prove well-posedness and regularity of a related switching system. The error bounds are based on estimates for the scheme near the boundary, where the standard regularisation procedure is not applicable, and are found to be of the same order as known results for the whole space. As special cases we deduce error bounds for finite difference and (truncated) semi-Lagrangian schemes.

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Dates et versions

hal-01626568 , version 1 (31-10-2017)

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  • HAL Id : hal-01626568 , version 1

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Athena Picarelli, Christoph Reisinger, Julen Rotaetxe Arto. Error bounds for monotone schemes for parabolic Hamilton-Jacobi-Bellman equations in bounded domains. 2017. ⟨hal-01626568⟩

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