L1 Error Estimates for Difference Approximations Of Degenerate Convection-Diffusion Equations

preprint2013arXivOpen access

Abstract

We analyze monotone difference schemes for strongly degenerate convection-diffusion equations in one spatial dimension. These nonlinear equations are well-posed within a class of (discontinuous) entropy solutions. We prove that the L1 difference between the approximate solutions and the unique entropy solution is bounded above by a constant times the cube root of the spatial discretization parameter.

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