A Mixed Formulation of the Monge-Kantorovich Equations

John W. Barrett; Leonid Prigozhin

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

  • Volume: 41, Issue: 6, page 1041-1060
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Barrett, John W., and Prigozhin, Leonid. "A Mixed Formulation of the Monge-Kantorovich Equations." ESAIM: Mathematical Modelling and Numerical Analysis 41.6 (2007): 1041-1060. <http://eudml.org/doc/250035>.

@article{Barrett2007,
abstract = { 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. },
author = {Barrett, John W., Prigozhin, Leonid},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Monge-Kantorovich problem; optimal transportation; mixed methods; finite elements; existence; convergence analysis.; mixed methods; convergence analysis},
language = {eng},
month = {12},
number = {6},
pages = {1041-1060},
publisher = {EDP Sciences},
title = {A Mixed Formulation of the Monge-Kantorovich Equations},
url = {http://eudml.org/doc/250035},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Barrett, John W.
AU - Prigozhin, Leonid
TI - A Mixed Formulation of the Monge-Kantorovich Equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2007/12//
PB - EDP Sciences
VL - 41
IS - 6
SP - 1041
EP - 1060
AB - 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.
LA - eng
KW - Monge-Kantorovich problem; optimal transportation; mixed methods; finite elements; existence; convergence analysis.; mixed methods; convergence analysis
UR - http://eudml.org/doc/250035
ER -

References

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