TY - JOUR T1 - Stability of Finite Difference Schemes for Hyperbolic Initial Boundary Value Problems: Numerical Boundary Layers 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 -

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.