We consider the initial value problem for degenerate viscous and inviscid scalar conservation laws where the flux function depends on the spatial location through a “rough” coefficient function . We show that the Engquist-Osher (and hence all monotone) finite difference approximations converge to the unique entropy solution of the governing equation if, among other demands, is in , thereby providing alternative (new) existence proofs for entropy solutions of degenerate convection-diffusion equations as well as new convergence results for their finite difference approximations. In the inviscid case, we also provide a rate of convergence. Our convergence proofs are based on deriving a series of a priori estimates and using a general compactness criterion.
@article{M2AN_2001__35_2_239_0,
author = {Karlsen, Kenneth Hvistendahl and Risebro, Nils Henrik},
title = {Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {35},
year = {2001},
pages = {239-269},
mrnumber = {1825698},
zbl = {1032.76048},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2001__35_2_239_0}
}
Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik. Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 35 (2001) pp. 239-269. http://gdmltest.u-ga.fr/item/M2AN_2001__35_2_239_0/
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