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Numerical homogenization of a linear multiscale conservation law
Abstract
We address the numerical approximation of a scalar conservation law with a highly oscillatory flux, in the linear setting. Taking advantage of the intrinsic numerical viscosity of the scheme employed that yields a parabolic regularization of the original hyperbolic equation, we use homogenization theory to derive an effective equation which in turn we solve numerically. Our numerical experiments show the performance of the approach on the example of the Lax-Friedrichs scheme.
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BibTeX
@misc{bris2026numerical,
title = {{Numerical homogenization of a linear multiscale conservation law}},
author = {Claude Le Bris and Frédéric Legoll and Giulia Merlini},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37546},
eprint = {2609.37546},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05770610v1},
}
RIS
TY - UNPB
TI - Numerical homogenization of a linear multiscale conservation law
AU - Claude Le Bris
AU - Frédéric Legoll
AU - Giulia Merlini
PY - 2026
DA - 2026/09/29
PB - HAL
DO - 10.48550/arxiv.2609.37546
UR - https://hal.science/hal-05770610v1
AB - We address the numerical approximation of a scalar conservation law with a highly oscillatory flux, in the linear setting. Taking advantage of the intrinsic numerical viscosity of the scheme employed that yields a parabolic regularization of the original hyperbolic equation, we use homogenization theory to derive an effective equation which in turn we solve numerically. Our numerical experiments show the performance of the approach on the example of the Lax-Friedrichs scheme.
ER -