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Uncertainty Quantification for the Homogeneous Landau-Fokker-Planck Equation via Deterministic Particle Galerkin methods
Rafael Bailo, José Antonio Carrillo, Andrea Medaglia +1
We design a deterministic particle method for the solution of the spatially homogeneous Landau equation with uncertainty. The deterministic particle approximation is based on the r…
A Finite-Volume Scheme for Fractional Diffusion on Bounded Domains
Rafael Bailo, José A. Carrillo, Stefano Fronzoni +1
We propose a new fractional Laplacian for bounded domains, expressed as a conservation law and thus particularly suited to finite-volume schemes. Our approach permits the direct pr…
Fully Discrete Positivity-Preserving and Energy-Dissipating Schemes for Aggregation-Diffusion Equations with a Gradient Flow Structure
Rafael Bailo, Jose A. Carrillo, Jingwei Hu
We propose fully discrete, implicit-in-time finite-volume schemes for a general family of non-linear and non-local Fokker-Planck equations with a gradient-flow structure, usually k…