Well-posedness of a non-local model for material flow on conveyor belts

Rossi, Elena ; Kötz, Jennifer ; Goatin, Paola ; Göttlich, Simone

Additional URL: https://hal.inria.fr/hal-02022654
Document Type: Working paper
Year of publication: 2019
Place of publication: Mannheim [u.a.]
Publication language: English
Institution: School of Business Informatics and Mathematics > Scientific Computing (Göttlich 2011-)
Subject: 510 Mathematics
Abstract: 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.

Dieser Eintrag ist Teil der Universitätsbibliographie.

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