A mixed finite element discretization of dynamical optimal transport
Numerical Analysis
2022-02-24 v4 Numerical Analysis
Abstract
In this paper we introduce a new class of finite element discretizations of the quadratic optimal transport problem based on its dynamical formulation. These generalize to the finite element setting the finite difference scheme proposed by Papadakis et al. [SIAM J Imaging Sci, 7(1):212--238,2014]. We solve the discrete problem using a proximal splitting approach and we show how to modify this in the presence of regularization terms which are relevant for physical data interpolation.
Cite
@article{arxiv.2003.04558,
title = {A mixed finite element discretization of dynamical optimal transport},
author = {Andrea Natale and Gabriele Todeschi},
journal= {arXiv preprint arXiv:2003.04558},
year = {2022}
}
Comments
Journal of Scientific Computing, Springer Verlag, In press