A high-resolution finite volume scheme based on optimal spectral properties of the fully discrete scheme with minimized dispersion and adaptive dissipation

2021 ◽  
pp. 105226
Author(s):  
Siye Li ◽  
Yu Hu ◽  
Zhensheng Sun ◽  
YiAng Shi ◽  
Kai Mao
Keyword(s):  
High Resolution ◽  
Finite Volume ◽  
Spectral Properties ◽  
Finite Volume Scheme ◽  
Discrete Scheme ◽  
Volume Scheme ◽  
Fully Discrete

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

2020 ◽  
Vol 30 (13) ◽  
pp. 2487-2522
Author(s):  
Rafael Bailo ◽  
José A. Carrillo ◽  
Hideki Murakawa ◽  
Markus Schmidtchen
Keyword(s):  
Finite Volume ◽  
Flow Structure ◽  
Gradient Flow ◽  
Diffusion Equations ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Discrete Energy ◽  
Volume Scheme ◽  
Fully Discrete ◽  
Local Aggregation

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.

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