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

Bokanowski, Olivier; Falcone, Maurizio; Ferretti, Roberto; Gr�ne, Lars; Kalise, Dante; Zidani, Hasnaa

Authors

Olivier Bokanowski

Maurizio Falcone

Roberto Ferretti

Lars Gr�ne

Dante Kalise

Hasnaa Zidani



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, ?-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.

Citation

Bokanowski, O., Falcone, M., Ferretti, R., Grüne, L., Kalise, D., & Zidani, H. (2015). Value iteration convergence of ε-monotone schemes for stationary Hamilton-Jacobi equations. Discrete and Continuous Dynamical Systems - Series A, 35(9), 4041-4070. https://doi.org/10.3934/dcds.2015.35.4041

Journal Article Type Article
Acceptance Date Oct 15, 2014
Online Publication Date Sep 1, 2015
Publication Date Sep 1, 2015
Deposit Date Nov 12, 2019
Publicly Available Date Mar 29, 2024
Journal Discrete and Continuous Dynamical Systems- Series A
Print ISSN 1078-0947
Electronic ISSN 1553-5231
Publisher American Institute of Mathematical Sciences
Peer Reviewed Peer Reviewed
Volume 35
Issue 9
Pages 4041-4070
DOI https://doi.org/10.3934/dcds.2015.35.4041
Public URL https://nottingham-repository.worktribe.com/output/3220572