<div class="csl-bib-body">
<div class="csl-entry">Jüngel, A., & Vetter, M. (2023). A Convergent Entropy-Dissipating BDF2 Finite-Volume Scheme for a Population Cross-Diffusion System. <i>Computational Methods in Applied Mathematics</i>, <i>24</i>(3), 725–746. https://doi.org/10.1515/cmam-2023-0009</div>
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dc.identifier.issn
1609-4840
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/190252
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dc.description.abstract
A second-order backward differentiation formula (BDF2) finite-volume discretization for a nonlinear cross-diffusion system arising in population dynamics is studied. The numerical scheme preserves the Rao entropy structure and conserves the mass. The existence and uniqueness of discrete solutions and their large-time behavior as well as the convergence of the scheme are proved. The proofs are based on the G-stability of the BDF2 scheme, which provides an inequality for the quadratic Rao entropy and hence suitable a priori estimates. The novelty is the extension of this inequality to the system case. Some numerical experiments in one and two space dimensions underline the theoretical results.
en
dc.language.iso
en
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dc.publisher
WALTER DE GRUYTER GMBH
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dc.relation.ispartof
Computational Methods in Applied Mathematics
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dc.subject
Cross-Diffusion Equations
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dc.subject
Discrete Entropy Dissipation
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dc.subject
Finite-Volume Method
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dc.subject
Linear Multistep Method
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dc.subject
Population Dynamics
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dc.subject
Rao Entropy
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dc.title
A Convergent Entropy-Dissipating BDF2 Finite-Volume Scheme for a Population Cross-Diffusion System
