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Cite Details

J. E. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, "Fourth- and sixth-order conservative finite difference approximations of the divergence and gradient", Applied Numerical Mathematics, vol. 37, no. 1-2, pp. 171--187, Apr 2001

Abstract

We derive conservative fourth- and sixth-order finite difference approximations for the divergence and gradient operators and a compatible inner product on staggered 1D uniform grids in a bounded domain. The methods combine standard centered difference formulas in the interior with new one-sided finite difference approximations near the boundaries. We derive compatible inner products for these difference methods that are high-order approximations of the continuum inner product. We also investigate defining compatible high-order divergence and gradient finite difference operators that satisfy a discrete integration by parts identity.

BibTeX Entry

@article{castillo-2001-fourth,
author = {J. E. Castillo and J. M. Hyman and M. Shashkov and S. Steinberg},
title = {Fourth- and sixth-order conservative finite difference approximations of the divergence and gradient},
year = {2001},
month = Apr,
urlpdf = {http://math.lanl.gov/~mac/papers/numerics/CHSS01.pdf},
journal = {Applied Numerical Mathematics},
volume = {37},
number = {1-2},
pages = {171--187}
}