Implicit monotone difference methods for scalar conservation laws with source terms
Analysis of PDEs
2016-09-29 v1
Abstract
In this article, a concept of implicit methods for scalar conservation laws in one or more spatial dimensions allowing also for source terms of various types is presented. This material is a significant extension of previous work of the first author [3]. Implicit notions are developed that are centered around a monotonicity criterion. We demonstrate a connection between a numerical scheme and a discrete entropy inequality, which is based on a classical approach by Crandall and Majda. Additionally, three implicit methods are investigated using the developed notions. Next, we conduct a convergence proof which is not based on a classical compactness argument. Finally, the theoretical results are confirmed by various numerical tests.
Cite
@article{arxiv.1609.08861,
title = {Implicit monotone difference methods for scalar conservation laws with source terms},
author = {Michael Breuß and Andreas Kleefeld},
journal= {arXiv preprint arXiv:1609.08861},
year = {2016}
}