A mixed formulation of the Monge-Kantorovich equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 6, p. 1041-1060

We introduce and analyse a mixed formulation of the Monge-Kantorovich equations, which express optimality conditions for the mass transportation problem with cost proportional to distance. Furthermore, we introduce and analyse the finite element approximation of this formulation using the lowest order Raviart-Thomas element. Finally, we present some numerical experiments, where both the optimal transport density and the associated Kantorovich potential are computed for a coupling problem and problems involving obstacles and regions of cheap transportation.

DOI : https://doi.org/10.1051/m2an:2007051
Classification:  35D05,  35J85,  49J40,  65N12,  65N30,  82B27
Keywords: Monge-kantorovich problem, optimal transportation, mixed methods, finite elements, existence, convergence analysis
@article{M2AN_2007__41_6_1041_0,
author = {Barrett, John W. and Prigozhin, Leonid},
title = {A mixed formulation of the Monge-Kantorovich equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {41},
number = {6},
year = {2007},
pages = {1041-1060},
doi = {10.1051/m2an:2007051},
zbl = {1132.35333},
mrnumber = {2377106},
language = {en},
url = {http://www.numdam.org/item/M2AN_2007__41_6_1041_0}
}

Barrett, John W.; Prigozhin, Leonid. A mixed formulation of the Monge-Kantorovich equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 6, pp. 1041-1060. doi : 10.1051/m2an:2007051. http://www.numdam.org/item/M2AN_2007__41_6_1041_0/

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