Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients
Kenneth Hvistendahl Karlsen, Nils Henrik Risebro (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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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...