Skip to main content
    • Aa
    • Aa

Stability of Finite Difference Schemes for Hyperbolic Initial Boundary Value Problems: Numerical Boundary Layers

  • Benjamin Boutin (a1) and Jean-François Coulombel (a2)

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.

Corresponding author
*Corresponding author. Email addresses: (B. Boutin), (J. F. Coulombel)
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1] R. Courant , K. Friedrichs and H. Lewy , Über die partiellen differenzengle-ichungen der mathematischen physik, Math. Ann., 100(1) (1928), pp. 3274.

[2] J. F. Coulombel and A. Gloria , Semigroup stability of finite difference schemes for multidimensional hyperbolic initial boundary value problems, Math. Comp., 80(273) (2011), pp. 165203.

[3] C. Chainais-Hillairet and E. Grenier , Numerical boundary layers for hyperbolic systems in 1-D, M2AN Math. Model. Numer. Anal., 35(1) (2001), pp. 91106.

[6] F. Dubois and P. LeFloch , Boundary conditions for nonlinear hyperbolic systems of conservation laws, J. Differ. Equations, 71(1)(1988), pp. 93122.

[9] M. Gisclon and D. Serre , Conditions aux limites pour un système strictement hyperbolique fournies par le schéma de Godunov, RAIRO Modél. Math. Anal. Numér., 31(3) (1997), pp. 359380.

[10] M. Goldberg and E. Tadmor , Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems. II, Math. Comp., 36(154) (1981), pp. 603626.

[11] B. Gustafsson , The convergence rate for difference approximations to mixed initial boundary value problems, Math. Comp., 29(130) (1975), pp. 396406.

[15] H. O. Kreiss , Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math., 23 (1970), pp. 277298.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Numerical Mathematics: Theory, Methods and Applications
  • ISSN: 1004-8979
  • EISSN: 2079-7338
  • URL: /core/journals/numerical-mathematics-theory-methods-and-applications
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 7 *
Loading metrics...

Abstract views

Total abstract views: 34 *
Loading metrics...

* Views captured on Cambridge Core between 20th June 2017 - 21st July 2017. This data will be updated every 24 hours.