We are concerned with fully-discrete schemes for the numerical approximation of diffusive-dispersive hyperbolic conservation laws with a discontinuous flux function in one-space dimension. More precisely, we show the convergence of approximate solutions, generated by the scheme corresponding to vanishing diffusive-dispersive scalar conservation laws with a discontinuous coefficient, to the corresponding scalar conservation law with discontinuous coefficient. Finally, the convergence is illustrated by several examples. In particular, it is delineated that the limiting solutions generated by the scheme need not coincide, depending on the relation between diffusion and the dispersion coefficients, with the classical Kružkov−Oleĭnik entropy solutions, but contain nonclassical undercompressive shock waves.
Accepté le :
DOI : 10.1051/m2an/2015083
Mots clés : Conservation laws, discontinuous flux, diffusive-dispersive approximation, finite difference scheme, convergence, entropy condition, nonclassical shock
@article{M2AN_2016__50_5_1289_0,
author = {Dutta, Rajib and Koley, Ujjwal and Ray, Deep},
title = {Convergence of fully discrete schemes for diffusive dispersive conservation laws with discontinuous coefficient},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1289--1331},
publisher = {EDP-Sciences},
volume = {50},
number = {5},
year = {2016},
doi = {10.1051/m2an/2015083},
zbl = {1373.65054},
mrnumber = {3554544},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2015083/}
}
TY - JOUR AU - Dutta, Rajib AU - Koley, Ujjwal AU - Ray, Deep TI - Convergence of fully discrete schemes for diffusive dispersive conservation laws with discontinuous coefficient JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 1289 EP - 1331 VL - 50 IS - 5 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2015083/ DO - 10.1051/m2an/2015083 LA - en ID - M2AN_2016__50_5_1289_0 ER -
%0 Journal Article %A Dutta, Rajib %A Koley, Ujjwal %A Ray, Deep %T Convergence of fully discrete schemes for diffusive dispersive conservation laws with discontinuous coefficient %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 1289-1331 %V 50 %N 5 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2015083/ %R 10.1051/m2an/2015083 %G en %F M2AN_2016__50_5_1289_0
Dutta, Rajib; Koley, Ujjwal; Ray, Deep. Convergence of fully discrete schemes for diffusive dispersive conservation laws with discontinuous coefficient. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 5, pp. 1289-1331. doi : 10.1051/m2an/2015083. http://archive.numdam.org/articles/10.1051/m2an/2015083/
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