Barrett, John W.; Prigozhin, Leonid
A mixed formulation of the Monge-Kantorovich equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 41 (2007) no. 6 , p. 1041-1060
Zbl 1132.35333 | MR 2377106 | 1 citation dans Numdam
doi : 10.1051/m2an:2007051
URL stable :

Classification:  35D05,  35J85,  49J40,  65N12,  65N30,  82B27
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.


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