On the convergence rate of finite difference methods for degenerate convection-diffusion equations in several space dimensions

2014/11/17 by Kenneth Hvistendahl Karlsen, Kenneth H. Karlsen, Karlsen, Kenneth Hvistendahl +4
Engineering · Mathematics · #35L70 #65M06 #65M12 #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical methods for differential equations #math.AP #msc:35L70 #msc:65M06 #msc:65M12

paper · pdf · doi:10.48550/arxiv.1411.4538

openalex publication_date 2014/11/17 · arxiv created 2015/09/04 · arxiv updated 2015/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze upwind difference methods for strongly degenerate convection-diffusion equations in several spatial dimensions. We prove that the local L¹-error between the exact and numerical solutions is O(Δx^2/(19+d)), where d is the spatial dimension and Δx is the grid size. The error estimate is robust with respect to vanishing diffusion effects. The proof makes effective use of specific kinetic formulations of the difference method and the convection-diffusion equation.

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