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Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients

Kenneth Hvistendahl KarlsenNils Henrik Risebro — 2001

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

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 k ( x ) . 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, k ' is in B V , thereby providing alternative (new) existence proofs for entropy solutions of degenerate convection-diffusion equations...

Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients

Kenneth Hvistendahl KarlsenNils Henrik Risebro — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

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...

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