Stability of Finite Difference Schemes for Hyperbolic Initial Boundary Value Problems: Numerical Boundary Layers. Issue 3 (20th June 2017)

• Record Type: Journal Article
• Authors: Boutin, Benjamin; Coulombel, Jean-François
• Is Part Of: Numerical mathematics. Volume 10:Issue 3(2017)
• Page Start: 489
• Page End: 519
• Publication Date: 2017-06-20
• Subjects: 65M12, -- 65M06, -- 65M20; Transport equations, -- numerical schemes, -- Dirichlet boundary condition, -- boundary layers, -- stability; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.4208/nmtma.2017.m1525
• Languages: English
• ISSNs: 1004-8979

Abstract

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.