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arXiv · 1811.02229

The Neumann numerical boundary condition for transport equations

Jean-François Coulombel·Frédéric Lagoutière
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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.

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Jean-François Coulombel, Frédéric Lagoutière. 2018-11-06. The Neumann numerical boundary condition for transport equations. https://arxiv.org/abs/1811.02229

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