A new variational finite volume discretization for Wasserstein gradient flows that guarantees non-negativity and energy decay, with uniqueness for convex energies and convergence proved for the linear Fokker-Planck equation under positive initial density.
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2019 2verdicts
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Four finite volume schemes based on different flux formulations are proposed for a degenerated drift-diffusion system, with stability and existence shown for all four and convergence proven for two, plus numerical experiments.
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A variational finite volume scheme for Wasserstein gradient flows
A new variational finite volume discretization for Wasserstein gradient flows that guarantees non-negativity and energy decay, with uniqueness for convex energies and convergence proved for the linear Fokker-Planck equation under positive initial density.
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A numerical analysis focused comparison of several Finite Volume schemes for an Unipolar Degenerated Drift-Diffusion Model
Four finite volume schemes based on different flux formulations are proposed for a degenerated drift-diffusion system, with stability and existence shown for all four and convergence proven for two, plus numerical experiments.