Journal Article

FZJ-2020-00128

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Implicit Monotone Difference Methods for Scalar Conservation Laws with Source Terms

Breuß, M. ; Kleefeld, A. (Corresponding author)FZJ*

2020
Springer Singapore Singapore

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Please use a persistent id in citations: http://hdl.handle.net/2128/25613  doi:10.1007/s40306-019-00354-1

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 (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.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 511 - Computational Science and Mathematical Methods (POF3-511) (POF3-511)

Appears in the scientific report 2020

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Database coverage:
; Clarivate Analytics Master Journal List ; Emerging Sources Citation Index ; SCOPUS ; Web of Science Core Collection

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