**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",

}