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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.
@article{M2AN_2001__35_1_91_0,
author = {Chainais-Hillairet, Claire and Grenier, Emmanuel},
title = {Numerical boundary layers for hyperbolic systems in {1-D}},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {91--106},
publisher = {EDP-Sciences},
volume = {35},
number = {1},
year = {2001},
mrnumber = {1811982},
zbl = {0980.65093},
language = {en},
url = {http://geodesic.mathdoc.fr/item/M2AN_2001__35_1_91_0/}
}
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 PY - 2001 SP - 91 EP - 106 VL - 35 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/item/M2AN_2001__35_1_91_0/ LA - en ID - M2AN_2001__35_1_91_0 ER -
%0 Journal Article %A Chainais-Hillairet, Claire %A Grenier, Emmanuel %T Numerical boundary layers for hyperbolic systems in 1-D %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2001 %P 91-106 %V 35 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/item/M2AN_2001__35_1_91_0/ %G en %F M2AN_2001__35_1_91_0
Chainais-Hillairet, Claire; Grenier, Emmanuel. Numerical boundary layers for hyperbolic systems in 1-D. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 1, pp. 91-106. http://geodesic.mathdoc.fr/item/M2AN_2001__35_1_91_0/