H-box methods for the approximation of one-dimensional conservation laws on irregular grids
by M. J. Berger, C. Helzel and R. J. LeVeque SIAM J. Numer. Anal., 41 (2003), pp. 893-918.

Abstract. We study generalizations of the high-resolution wave propagation algorithm for the approximation of hyperbolic conservation laws on irregular grids that have a time step restriction based on a reference grid cell length that can be orders of magnitude larger than the smallest grid cell arising in the discretization. This Godunov-type scheme calculates fluxes at cell interfaces by solving Riemann problems defined over boxes of a reference grid cell length h. We discuss stability and accuracy of the resulting so-called h-box methods for one-dimensional systems of conservation laws. An extension of the method for the two-dimensional case, which is based on the multidimensional wave propagation algorithm, is also described.
Key words. finite volume methods, conservation laws, nonuniform grids, stability, accuracy

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bibtex entry:
@Article{mjb-hel-rjl:hbox,
author = "M. J. Berger and C. Helzel and R. J. LeVeque",
title = "{H}-box methods for the approximation of
one-dimensional conservation laws on irregular grids",
journal = "SIAM J. Numer. Anal.",
volume = "41",
year = "2003",
pages = "893--918",
URL = "http://epubs.siam.org/sam-bin/dbq/article/40539",
}