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 -error estimates for numerical approximations of Hamilton-Jacobi-Bellman equations in dimension 1
Author(s):
Olivier
Bokanowski;
Nicolas
Forcadel;
Hasnaa
Zidani.
Journal:
Math. Comp.
79
(2010),
1395-1426.
MSC (2000):
Primary 49L99, 65M15
Posted:
January 13, 2010
MathSciNet review:
2629998
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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  -error estimates for both schemes. We also provide numerical examples to validate their accuracy in solving smooth and discontinuous solutions.
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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
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
DOI:
10.1090/S0025-5718-10-02311-2
PII:
S 0025-5718(10)02311-2
Keywords:
Hamilton-Jacobi-Bellman equations,
lower semicontinuous viscosity solutions,
Fast Marching Method,
Ultra-Bee scheme,
$L^1$-error estimate,
anti-diffusive scheme,
comparison principle.
Received by editor(s):
April 7, 2008
Received by editor(s) in revised form:
February 4, 2009
Posted:
January 13, 2010
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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