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

  • Kenneth Hvistendahl Karlsen (a1) and Nils Henrik Risebro (a2)

Abstract

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 BV, 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 Lp compactness criterion.

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

  • Kenneth Hvistendahl Karlsen (a1) and Nils Henrik Risebro (a2)

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