Article Dans Une Revue Mathematical Models and Methods in Applied Sciences Année : 2020

Convergence of a fully discrete and energy-dissipating finite-volume scheme for aggregation-diffusion equations

Résumé

We study an implicit finite-volume scheme for non-linear, non-local aggregation-diffusion equations which exhibit a gradient-flow structure, recently introduced in [3]. Crucially, this scheme keeps the dissipation property of an associated fully discrete energy, and does so unconditionally with respect to the time step. Our main contribution in this work is to show the convergence of the method under suitable assumptions on the diffusion functions and potentials involved.

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hal-03125839 , version 1 (29-01-2021)

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Rafael Bailo, José A. Carrillo, Hideki Murakawa, Markus Schmidtchen. Convergence of a fully discrete and energy-dissipating finite-volume scheme for aggregation-diffusion equations. Mathematical Models and Methods in Applied Sciences, 2020, 30 (13), pp.2487-2522. ⟨10.1142/S0218202520500487⟩. ⟨hal-03125839⟩
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