Convergence order of upwind type schemes for transport equations with discontinuous coefficients
Numerical Analysis
2016-02-19 v1 Analysis of PDEs
Abstract
An analysis of the error of the upwind scheme for transport equation with discontinuous coefficients is provided. We consider here a velocity field that is bounded and one-sided Lipschitz continuous. In this framework, solutions are defined in the sense of measures along the lines of Poupaud and Rascle's work. We study the convergence order of the upwind scheme in the Wasserstein distances. More precisely, we prove that in this setting the convergence order is 1/2. We also show the optimality of this result. In the appendix, we show that this result also applies to other "diffusive" "first order" schemes and to a forward semi-Lagrangian scheme.
Keywords
Cite
@article{arxiv.1602.05746,
title = {Convergence order of upwind type schemes for transport equations with discontinuous coefficients},
author = {François Delarue and Frédéric Lagoutière and Nicolas Vauchelet},
journal= {arXiv preprint arXiv:1602.05746},
year = {2016}
}