L1 Error Estimates for Difference Approximations Of Degenerate Convection-Diffusion Equations
Analysis of PDEs
2013-04-16 v2
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.
Keywords
Cite
@article{arxiv.1205.0907,
title = {L1 Error Estimates for Difference Approximations Of Degenerate Convection-Diffusion Equations},
author = {Kenneth H. Karlsen and Nils Henrik Risebro and Erlend B. Storrøsten},
journal= {arXiv preprint arXiv:1205.0907},
year = {2013}
}