Compactness estimates for difference schemes for conservation laws with discontinuous flux
Numerical Analysis
2023-10-31 v2 Numerical Analysis
Abstract
We establish quantitative compactness estimates for finite difference schemes used to solve nonlinear conservation laws. These equations involve a flux function , where the coefficient is -regular and may exhibit discontinuities along curves in the plane. Our approach, which is technically elementary, relies on a discrete interaction estimate and the existence of one entropy function. While the details are specifically outlined for the Lax-Friedrichs scheme, the same framework can be applied to other difference schemes. Notably, our compactness estimates are new even in the homogeneous case ().
Keywords
Cite
@article{arxiv.2305.18765,
title = {Compactness estimates for difference schemes for conservation laws with discontinuous flux},
author = {Kenneth H. Karlsen and John D. Towers},
journal= {arXiv preprint arXiv:2305.18765},
year = {2023}
}