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Journal Articles Numerical Mathematics: Theory, Methods and Applications Year : 2017

Stability of finite difference schemes for hyperbolic initial boundary value problems: numerical boundary layers

Abstract

In this article, we give a unified theory for constructing boundary layer expansions for discretized transport equations with homogeneous Dirichlet boundary conditions. We exhibit a natural assumption on the discretization under which the numerical solution can be written approximately as a two-scale boundary layer expansion. In particular, this expansion yields discrete semigroup estimates that are compatible with the continuous semigroup estimates in the limit where the space and time steps tend to zero. The novelty of our approach is to cover numerical schemes with arbitrarily many time levels, while semigroup estimates were restricted, up to now, to numerical schemes with two time levels only.
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Dates and versions

hal-01114666 , version 1 (09-02-2015)
hal-01114666 , version 2 (16-06-2023)

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Benjamin Boutin, Jean-François Coulombel. Stability of finite difference schemes for hyperbolic initial boundary value problems: numerical boundary layers. Numerical Mathematics: Theory, Methods and Applications, 2017, 10 (3), pp.489-519. ⟨10.4208/nmtma.2017.m1525⟩. ⟨hal-01114666v2⟩
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