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

2012/05/04 by Kenneth H. Karlsen, Karlsen, Kenneth H., Nils Henrik Risebro +3
Mathematics · #35L65 (Secondary) #65M06 #65M15 (Primary) 35K65 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35K65 #msc:35L65 #msc:65M06 #msc:65M15

paper · pdf · doi:10.48550/arxiv.1205.0907

arxiv created 2013/04/15 · arxiv updated 2013/04/16

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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