Work

Numerical homogenization of a linear multiscale conservation law

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.37546

Authors: Bris, Claude Le, Legoll, Frédéric, Merlini, Giulia

Institutions: Centre National de la Recherche Scientifique, École nationale des ponts et chaussées, Institut Polytechnique de Paris, MATHERIALS: MATHematics for MatERIALS, Institut national de recherche en sciences et technologies du numérique

Language: English

Topic: Advanced Mathematical Modeling in Engineering

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Office of Naval Research, European Office of Aerospace Research and Development

OpenAlex ID: W7214904283

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