This title appears in the Scientific Report :
2020
Please use the identifier:
http://dx.doi.org/10.1007/s40306-019-00354-1 in citations.
Please use the identifier: http://hdl.handle.net/2128/25613 in citations.
Implicit Monotone Difference Methods for Scalar Conservation Laws with Source Terms
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)....
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Personal Name(s): | Breuß, Michael |
---|---|
Kleefeld, Andreas (Corresponding author) | |
Contributing Institute: |
Jülich Supercomputing Center; JSC |
Published in: | Acta mathematica Vietnamica, 45 (2020) 3, S. 709–738 |
Imprint: |
Singapore
Springer Singapore
2020
|
DOI: |
10.1007/s40306-019-00354-1 |
Document Type: |
Journal Article |
Research Program: |
Computational Science and Mathematical Methods |
Link: |
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Publikationsportal JuSER |
Please use the identifier: http://hdl.handle.net/2128/25613 in citations.
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. |