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

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

Abstract

We study an implicit finite-volume scheme for nonlinear, non-local aggregation-diffusion equations which exhibit a gradient-flow structure, recently introduced in [R. Bailo, J. A. Carrillo and J. Hu, Fully discrete positivity-preserving and energy-dissipating schemes for aggregation-diffusion equations with a gradient flow structure, arXiv:1811.11502]. 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.

Details

OriginalspracheEnglisch
Seiten (von - bis)2487-2522
Seitenumfang36
FachzeitschriftMathematical models and methods in applied sciences
Jahrgang30
Ausgabenummer13
PublikationsstatusVeröffentlicht - 2020
Peer-Review-StatusJa

Externe IDs

Scopus 85096165268

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Bibliotheksschlagworte