no. 1
Numerical boundary layers for hyperbolic systems in 1-D
ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 1, pp. 91-106

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.

Classification : 65M, 35L
Keywords: boundary layers stability 
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     author = {Chainais-Hillairet, Claire and Grenier, Emmanuel},
     title = {Numerical boundary layers for hyperbolic systems in {1-D}},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {91--106},
     year = {2001},
     publisher = {EDP Sciences},
     volume = {35},
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     mrnumber = {1811982},
     zbl = {0980.65093},
     language = {en},
     url = {https://www.numdam.org/item/M2AN_2001__35_1_91_0/}
}
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Chainais-Hillairet, Claire; Grenier, Emmanuel. Numerical boundary layers for hyperbolic systems in 1-D. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 1, pp. 91-106. https://www.numdam.org/item/M2AN_2001__35_1_91_0/

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