Implicit monotone difference methods for scalar conservation laws with source terms
- 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 (Breuß SIAM J. Numer. Anal. 43(3), 970–986 2005). 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.
Author: | Michael Breuß, Andreas KleefeldORCiD |
---|---|
DOI: | https://doi.org/10.1007/s40306-019-00354-1 |
ISSN: | 2315-4144 |
Parent Title (English): | Acta Mathematica Vietnamica |
Publisher: | Springer Singapore |
Place of publication: | Singapore |
Document Type: | Article |
Language: | English |
Year of Completion: | 2020 |
Date of first Publication: | 2020/01/10 |
Tag: | Conservation laws; Entropy solution; Finite difference methods; Implicit methods; Monotone methods; Source term |
Volume: | 45 |
First Page: | 709 |
Last Page: | 738 |
Note: | Corresponding author: Andreas Kleefeld |
Link: | https://doi.org/10.1007/s40306-019-00354-1 |
Zugriffsart: | campus |
Institutes: | FH Aachen / Fachbereich Medizintechnik und Technomathematik |
collections: | Verlag / Springer Singapore |