Some methods for the numerical approximation of time-dependent and steady first-order Hamilton-Jacobi equations are reviewed. Most of the discussion focuses on conformal triangular-type meshes, but we show how to extend this to the most general meshes. We review some first-order monotone schemes and also high-order ones specially dedicated to steady problems.
@article{bwmeta1.element.bwnjournal-article-amcv17i3p403bwm,
author = {Abgrall, R\'emi and Perrier, Vincent},
title = {On the numerical approximation of first-order Hamilton-Jacobi equations},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {17},
year = {2007},
pages = {403-412},
zbl = {1147.65323},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv17i3p403bwm}
}
Abgrall, Rémi; Perrier, Vincent. On the numerical approximation of first-order Hamilton-Jacobi equations. International Journal of Applied Mathematics and Computer Science, Tome 17 (2007) pp. 403-412. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv17i3p403bwm/
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