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https://dspace.ctu.edu.vn/jspui/handle/123456789/100893
Title: | Implicit monotone difference methods for scalar conservation laws with source terms |
Authors: | Breuß, Michael Kleefeld, Andreas |
Keywords: | Conservation laws Finite difference methods Implicit methods Monotone methods Source term Entropy solution |
Issue Date: | 2020 |
Series/Report no.: | Acta mathematica Vietnamica journal;Vol.45, No.03 .- P.709-738 |
Abstract: | In this article, a concept of implicit methods for sealar 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 (Breuß SIAM J. Numer. Anal. 43(3), 970-986 2005). Implicit notions are developed that are centered around a mono- tonicity 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. |
URI: | https://dspace.ctu.edu.vn/jspui/handle/123456789/100893 |
ISSN: | 0251-4184 |
Appears in Collections: | Acta Mathematica Vietnamica |
Files in This Item:
File | Description | Size | Format | |
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