# The Neumann numerical boundary condition for transport equations

2 MMCS - Modélisation mathématique, calcul scientifique
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : In this article, we show that prescribing homogeneous Neumann type numerical boundary conditions at an outflow boundary yields a convergent discretization in $\ell^\infty$ for transport equations. We show in particular that the Neumann numerical boundary condition is a stable, local, and absorbing numerical boundary condition for discretized transport equations. Our main result is proved for explicit two time level numerical approximations of transport operators with arbitrarily wide stencils. The proof is based on the energy method and bypasses any normal mode analysis.
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Cited literature [31 references]

https://hal.archives-ouvertes.fr/hal-01902551
Contributor : Jean-François Coulombel <>
Submitted on : Monday, November 5, 2018 - 11:41:33 AM
Last modification on : Friday, January 10, 2020 - 9:09:00 PM
Long-term archiving on: Wednesday, February 6, 2019 - 1:29:14 PM

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### Identifiers

• HAL Id : hal-01902551, version 2
• ARXIV : 1811.02229

### Citation

Jean-François Coulombel, Frédéric Lagoutière. The Neumann numerical boundary condition for transport equations. Kinetic and Related Models , AIMS, 2020, 13 (1), pp.1-32. ⟨hal-01902551v2⟩

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