Published 2020
| Version v1
Journal article
Well-posedness of a non-local model for material flow on conveyor belts
- Others:
- Analysis and Control of Unsteady Models for Engineering Sciences (ACUMES) ; Inria Sophia Antipolis - Méditerranée (CRISAM) ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
- Department of Mathematics and Computer Science [Mannheim] ; Universität Mannheim [Mannheim]
Description
In this paper, we focus on finite volume approximation schemes to solve a non-local material flow model in two space dimensions. Based on the numerical discretisation with dimensional splitting, we prove the convergence of the approximate solutions, where the main difficulty arises in the treatment of the discontinuity occurring in the flux function. In particular, we compare a Roe-type scheme to the well-established Lax-Friedrichs method and provide a numerical study highlighting the benefits of the Roe discretisation. Besides, we also prove the L1-Lipschitz continuous dependence on the initial datum, ensuring the uniqueness of the solution.
Abstract
MSC: 35L65, 65M12
Abstract
International audience
Additional details
- URL
- https://hal.inria.fr/hal-02022654
- URN
- urn:oai:HAL:hal-02022654v1
- Origin repository
- UNICA