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The Neumann numerical boundary condition for transport equations

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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https://hal.archives-ouvertes.fr/hal-01902551
Contributor : Jean-François Coulombel Connect in order to contact the contributor
Submitted on : Monday, November 5, 2018 - 11:41:33 AM
Last modification on : Tuesday, January 4, 2022 - 6:28:34 AM
Long-term archiving on: : Wednesday, February 6, 2019 - 1:29:14 PM

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  • 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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