- Abstract:
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In this work we present the convergence of a positivity preserving semi-discrete finite volume scheme for a coupled system of two non-local partial differential equations with cross-diffusion. The key to proving the convergence result is to establish positivity in order to obtain a discrete energy estimate to obtain compactness. We numerically observe the convergence to reference solutions with a first order accuracy in space. Moreover we recover segregated stationary states in spite of the r...
Expand abstract - Publication status:
- Published
- Peer review status:
- Peer reviewed
- Files:
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(, 0.0b)
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- Publisher copy:
- 10.1007/s00211-020-01121-3
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- Publisher:
- Springer Verlag Publisher's website
- Journal:
- Numerische Mathematik Journal website
- Volume:
- 145
- Issue:
- 3
- Pages:
- 473–511
- Publication date:
- 2020-05-26
- Acceptance date:
- 2020-05-02
- DOI:
- EISSN:
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0945-3245
- ISSN:
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0029-599X
- Pubs id:
-
1102650
- Local pid:
- pubs:1102650
- Language:
- English
- Keywords:
- Copyright holder:
- Carrillo et al.
- Copyright date:
- 2020
- Rights statement:
- © The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
- License:
- CC Attribution (CC BY)
Journal article
Convergence of a finite volume scheme for a system of interacting species with cross-diffusion
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