TY - JOUR
T1 - Stability of Finite Difference Schemes for Hyperbolic Initial Boundary Value Problems: Numerical Boundary Layers
AU - Benjamin Boutin & Jean-François Coulombel
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 489
EP - 519
PY - 2017
DA - 2017/10
SN - 10
DO - http://doi.org/10.4208/nmtma.2017.m1525
UR - https://global-sci.org/intro/article_detail/nmtma/12356.html
KW - 
AB - <p style="text-align: justify;">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.<br/></p>