$L^1$-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.References
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Additional Information
- Olivier Bokanowski
- Affiliation: Laboratoire Jacques-Louis Lions, Université Paris 6, 75252 Paris Cedex 05, and UFR de Mathématiques, Université Paris Diderot, Case 7012, 75251 Paris Cedex 05, France; and Projet Commands, INRIA Saclay & ENSTA, 32 Bd Victor, 75739 Paris Cedex 15, France
- MR Author ID: 605144
- Email: boka@math.jussieu.fr
- Nicolas Forcadel
- Affiliation: Ceremade, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, F-75775 Paris Cedex 16, France
- Email: forcadel@ceremade.dauphine.fr
- Hasnaa Zidani
- Affiliation: Projet Commands, INRIA Saclay & ENSTA, 32 Bd Victor, 75739 Paris Cedex 15, France
- Email: Hasnaa.Zidani@ensta.fr
- Received by editor(s): April 7, 2008
- Received by editor(s) in revised form: February 4, 2009
- Published electronically: January 13, 2010
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 79 (2010), 1395-1426
- MSC (2000): Primary 49L99, 65M15
- DOI: https://doi.org/10.1090/S0025-5718-10-02311-2
- MathSciNet review: 2629998