Numerical boundary layers for hyperbolic systems in 1-D

Claire Chainais-Hillairet; Emmanuel Grenier

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2001)

  • Volume: 35, Issue: 1, page 91-106
  • ISSN: 0764-583X

Abstract

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The aim of this paper is to investigate the stability of boundary layers which appear in numerical solutions of hyperbolic systems of conservation laws in one space dimension on regular meshes. We prove stability under a size condition for Lax Friedrichs type schemes and inconditionnal stability in the scalar case. Examples of unstable boundary layers are also given.

How to cite

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Chainais-Hillairet, Claire, and Grenier, Emmanuel. "Numerical boundary layers for hyperbolic systems in 1-D." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 35.1 (2001): 91-106. <http://eudml.org/doc/194046>.

@article{Chainais2001,
abstract = {The aim of this paper is to investigate the stability of boundary layers which appear in numerical solutions of hyperbolic systems of conservation laws in one space dimension on regular meshes. We prove stability under a size condition for Lax Friedrichs type schemes and inconditionnal stability in the scalar case. Examples of unstable boundary layers are also given.},
author = {Chainais-Hillairet, Claire, Grenier, Emmanuel},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {boundary layers stability; hyperbolic systems of conservation laws; Lax-Friedrichs scheme; numerical examples},
language = {eng},
number = {1},
pages = {91-106},
publisher = {EDP-Sciences},
title = {Numerical boundary layers for hyperbolic systems in 1-D},
url = {http://eudml.org/doc/194046},
volume = {35},
year = {2001},
}

TY - JOUR
AU - Chainais-Hillairet, Claire
AU - Grenier, Emmanuel
TI - Numerical boundary layers for hyperbolic systems in 1-D
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2001
PB - EDP-Sciences
VL - 35
IS - 1
SP - 91
EP - 106
AB - The aim of this paper is to investigate the stability of boundary layers which appear in numerical solutions of hyperbolic systems of conservation laws in one space dimension on regular meshes. We prove stability under a size condition for Lax Friedrichs type schemes and inconditionnal stability in the scalar case. Examples of unstable boundary layers are also given.
LA - eng
KW - boundary layers stability; hyperbolic systems of conservation laws; Lax-Friedrichs scheme; numerical examples
UR - http://eudml.org/doc/194046
ER -

References

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  10. [10] T.T. Li and W.C. Yu, Boundary value problems for quasilinear hyperbolic systems. Math. series V. Duke Univ., Durham (1985). Zbl0627.35001
  11. [11] T.P. Liu, Nonlinear stability of shock waves for viscous conservation laws. Mem. Amer. Math. Soc. 56 (1985) 108 p. Zbl0617.35058MR791863
  12. [12] J.B. Rauch and F.J. Massey, III, Differentiability of solutions to hyperbolic initial boundary value problems. Trans. Amer. Math. Soc. 189 (1974) 303–318. Zbl0282.35014
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