Refine
Year of publication
- 2020 (59) (remove)
Institute
- Fachbereich Medizintechnik und Technomathematik (59) (remove)
Has Fulltext
- no (59)
Document Type
- Article (44)
- Part of a Book (7)
- Conference Proceeding (4)
- Doctoral Thesis (2)
- Book (1)
- Other (1)
Keywords
- Adaptive control (1)
- Brownian Pillow (1)
- Choleratoxin B (1)
- Conservation laws (1)
- Crámer–von-Mises distance (1)
- Dimensional splitting (1)
- Entropy solution (1)
- Exponential time differencing (1)
- Finite difference methods (1)
- Higher-order codes (1)
Is part of the Bibliography
- no (59)
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.