3 papers
math.NA2020
Computation of Optimal Transport with Finite Volumes
Andrea Natale, Gabriele Todeschi
We construct Two-Point Flux Approximation (TPFA) finite volume schemes to solve the quadratic optimal transport problem in its dynamic form, namely the problem originally introduce…
math.NA2020
TPFA Finite Volume Approximation of Wasserstein Gradient Flows
Andrea Natale, Gabriele Todeschi
Numerous infinite dimensional dynamical systems arising in different fields have been shown to exhibit a gradient flow structure in the Wasserstein space. We construct Two Point Fl…
math.NA2019
A variational finite volume scheme for Wasserstein gradient flows
Clément Cancès, Thomas O. Gallouët, Gabriele Todeschi
We propose a variational finite volume scheme to approximate the solutions to Wasserstein gradient flows. The time discretization is based on an implicit linearization of the Wasse…