TPFA Finite Volume Approximation of Wasserstein Gradient Flows
Numerical Analysis
2020-06-29 v2 Numerical Analysis
Abstract
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 Flux Approximation Finite Volume schemes discretizing such problems which preserve the variational structure and have second order accuracy in space. We propose an interior point method to solve the discrete variational problem, providing an efficient and robust algorithm. We present two applications to test the scheme and show its order of convergence.
Keywords
Cite
@article{arxiv.2001.07005,
title = {TPFA Finite Volume Approximation of Wasserstein Gradient Flows},
author = {Andrea Natale and Gabriele Todeschi},
journal= {arXiv preprint arXiv:2001.07005},
year = {2020}
}