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Mathematics > Analysis of PDEs

arXiv:1811.02229 (math)
[Submitted on 6 Nov 2018]

Title:The Neumann numerical boundary condition for transport equations

Authors:Jean-François Coulombel (IMT), Frédéric Lagoutière (ICJ)
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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.
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1811.02229 [math.AP]
  (or arXiv:1811.02229v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1811.02229

Submission history

From: Jean-Francois Coulombel [view email] [via CCSD proxy]
[v1] Tue, 6 Nov 2018 08:57:20 UTC (33 KB)
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