TY  - JOUR
A1  - Breuß, Michael
A1  - Kleefeld, Andreas
T1  - Implicit monotone difference methods for scalar conservation laws with source terms
T2  - Acta Mathematica Vietnamica
N2  - 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.
KW  - Entropy solution
KW  - Source term
KW  - Monotone methods
KW  - Implicit methods
KW  - Finite difference methods
KW  - Conservation laws
Y1  - 2024
UR  - https://opus.bibliothek.fh-aachen.de/opus4/frontdoor/index/index/docId/11473
SN  - 2315-4144
N1  - Corresponding author: Andreas Kleefeld
VL  - 45
SP  - 709
EP  - 738
PB  - Springer Singapore
CY  - Singapore
ER  -