Value iteration convergence of ε-monotone schemes for stationary Hamilton-Jacobi equations

Olivier Bokanowski; Maurizio Falcone; Roberto Ferretti; Lars Grüne; Dante Kalise; Hasnaa Zidani

doi:10.3934/dcds.2015.35.4041

Value iteration convergence of ε-monotone schemes for stationary Hamilton-Jacobi equations

Olivier Bokanowski
, Maurizio Falcone
, Roberto Ferretti
, Lars Grüne
, Dante Kalise
, Hasnaa Zidani

École Polytechnique

UPMC Université de Paris VI
Università di Roma
Università di Roma
University of Bayreuth
Austrian Academy of Sciences

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

We present an abstract convergence result for the fixed point approximation of stationary Hamilton-Jacobi equations. The basic assumptions on the discrete operator are invariance with respect to the addition of constants, ε-monotonicity and consistency. The result can be applied to various high-order approximation schemes which are illustrated in the paper. Several applications to Hamilton-Jacobi equations and numerical tests are presented.

Original language	English
Pages (from-to)	4041-4070
Number of pages	30
Journal	Discrete and Continuous Dynamical Systems
Volume	35
Issue number	9
DOIs	https://doi.org/10.3934/dcds.2015.35.4041
Publication status	Published - 1 Sept 2015

Keywords

Fixed point approximation schemes
Hamilton-Jacobi equation
High-order methods
ε-monotonicity

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abstract = "We present an abstract convergence result for the fixed point approximation of stationary Hamilton-Jacobi equations. The basic assumptions on the discrete operator are invariance with respect to the addition of constants, ε-monotonicity and consistency. The result can be applied to various high-order approximation schemes which are illustrated in the paper. Several applications to Hamilton-Jacobi equations and numerical tests are presented.",

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AU - Bokanowski, Olivier

AU - Falcone, Maurizio

AU - Ferretti, Roberto

AU - Grüne, Lars

AU - Kalise, Dante

AU - Zidani, Hasnaa

PY - 2015/9/1

Y1 - 2015/9/1

N2 - We present an abstract convergence result for the fixed point approximation of stationary Hamilton-Jacobi equations. The basic assumptions on the discrete operator are invariance with respect to the addition of constants, ε-monotonicity and consistency. The result can be applied to various high-order approximation schemes which are illustrated in the paper. Several applications to Hamilton-Jacobi equations and numerical tests are presented.

AB - We present an abstract convergence result for the fixed point approximation of stationary Hamilton-Jacobi equations. The basic assumptions on the discrete operator are invariance with respect to the addition of constants, ε-monotonicity and consistency. The result can be applied to various high-order approximation schemes which are illustrated in the paper. Several applications to Hamilton-Jacobi equations and numerical tests are presented.

KW - Fixed point approximation schemes

KW - Hamilton-Jacobi equation

KW - High-order methods

KW - ε-monotonicity

UR - https://www.scopus.com/pages/publications/84926658706

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DO - 10.3934/dcds.2015.35.4041

M3 - Article

AN - SCOPUS:84926658706

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SP - 4041

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JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

IS - 9

ER -

Value iteration convergence of ε-monotone schemes for stationary Hamilton-Jacobi equations

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Keywords

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