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 |
| Date of the Publication (Server): | 2024/07/10 |
| 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 |
