Journal Articles Mathematical Models and Methods in Applied Sciences Year : 2020

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

José A. Carrillo
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Hideki Murakawa
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Abstract

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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Dates and versions

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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