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Convergence of a finite volume scheme for a system of interacting species with cross-diffusion

Abstract:

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...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s00211-020-01121-3

Authors


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Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Queen's College
ORCID:
0000-0001-8819-4660
Schmidtchen, M More by this author
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:
0945-3245
ISSN:
0029-599X
Pubs id:
1102650
Local pid:
pubs:1102650

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