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An error estimate for the finite difference approximation to degenerate convection -diffusion equations

2011/02/02 by Kenneth H. Karlsen, K. H. Karlsen, Ujjwal Koley +6
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #Differential Equations and Numerical Methods #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1102.0493

22 pages

openalex publication_date 2011/02/02 · arxiv created 2012/09/18 · arxiv updated 2012/09/20 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We consider semi-discrete first-order finite difference schemes for a nonlinear degenerate convection-diffusion equations in one space dimension, and prove an L1 error estimate. Precisely, we show that the L1 loc difference between the approximate solution and the unique entropy solution converges at a rate O(\Deltax 1/11), where \Deltax is the spatial mesh size. If the diffusion is linear, we get the convergence rate O(\Deltax 1/2), the point being that the O is independent of the size of the diffusion

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